I think you should see her paediatrician and ask for a referal to a clinical psychologist who will be able to give you some advice. She will be at nursery and school before you know it, and she needs to be able to deal with that.
Another thing that might help is getting a Play Therapist involved.
Also any other thing that is 'one to one' but not with you. Just to wean her from the need for continual contact with you. So, for example, music lessons, or something similar (I know she's young for that - but I think you understand what I mean). Sometimes, if you have a private gym membership, you can have an instructor give you child one to one swimming lessons whilst you are in the gym - just an idea. But I think you need the psychologist first so that you go about it in the right way.
You are correct - there is a lot of information on the internet but since solutions vary with each child, that is where professional help is often required. When we sought "mental health support" via a child psychiatrist, she give us suggestions and ideas on how to best help our child. She did not work with our child; but with the entire family to help us help her. We did not know this was how therapy worked with children but apparently, this is quite common (the doctor gives ideas/plans/suggestions; the parents deliver the ideas/plans/suggestions). If you ever get a mental health professional who only wants to work with your child, then I would suggest that you find another one who will work with the entire family.
The only way to treat anxiety is to "lessen the anxiety" but that does not mean to eliminate it. So, if your family attends large social situations, then it would be expected that your daughter also attend. But, I would let her know what will happen at the event prior to attending, reassure her that you will be by her side and if necessary, retreat to a quiet place to allow her to calm down. Once I took our child to a live theatre production but she found it so overwhelming that we sought refuge in a back stairwell during intermission before returning to our seats for the second act. By the way, she loved that play. Your friends mean well but their experience with their children is not your experience with your child and so the "parenting" methods will differ. Those of us with children suffering from anxiety understand; I doubt if your friends will ever truly "get it" - not their fault - they are just not "walking in your shoes".
Your daughter will not be able to overcome this on her own (at least not at two years of age) so stay with her (even put your arms around her so she feels protected). As she becomes more comfortable, she will gradually move away from you but this can take several months or possibly years. When years are involved, this is when one seeks professional medical help. When dealing with anxiety, it is best to follow the lead of the child - she will let you know when she is ready to "move on". But right now you can do simple socializing things as taking her grocery shopping, going to the mall, visiting McDonald's, attending church/Sunday School, going to parks, going to public pools even if she does not swim, having playdates in your home with one other child, etc. The point is to socialize, socialize, socialize so that your daughter becomes more comfortable around people (even though she may cling to you and the two of you remain a distance from others). Experts call this "intervention" but it really is just over-socialization (we did this with our child for many, many years - and still do, to some extent). One simple thing that a friend of mine did was to wave at people from time to time (often in the car) - people that she did not know so that her child got used to interacting with others.
There are lots of books you can borrow from your public library or purchase on-line or bookstores re anxiety in children. Two I might suggest are "the highly sensitive child" by Elaine N. Aron and "Keys to Parenting Your Anxious Child" by Katharina Manassis. As I said, there are many others as well. I hope some of this information will be of help to you - as I have said, I've been in your situation and I know how hard it is (and yes, I cried many a tears). I wish you the best ...
Many Thanks for your reply jdtm,
I've searched the internet for childrens anxiety issues and there is a fair bit of information. None of them seem to suggest practical ways of handling it though. I don't feel we're ready to go down the route of seeking mental health support, though will give my Health Visitor a call.
What I really need to know is should I keep my daughter away from large social situations, where her anxiety is at it's worst. Also when she is anxious how much attention to pay to it - should I give her lots of cuddles and reassurance or should I ignore the fact she's screaming the place down. I am so aware that how I respond now can affect whether it will get better or worse in the future but just don't know what to do for the best. My friends tell me I mollycoddle her and should ignore this behaviour, their children are all very naturally outgoing though.
Is it better for my daughter to realise she has to overcome this on her own, or for me to stay by her side constantly?
I have been in your situation - actually it is not an uncommon one. Your daughter suffers from social anxiety - a disorder she inherited at conception/birth. You did not cause this nor did her father cause this - anxiety can be exacerbated by life experiences but they do not cause this. I suspect there is a history (perhaps on her father's side) of anxiety issues.
First, I might suggest that you google the phrase "toddlers and anxiety" or "social anxiety in children" or similar words/phrases to better understand this issue. Because social anxiety is such a common problem, you will get many, many hits. Then, it might be wise to speak to your daughter's pediatrician about this issue. If anxiety is the problem, then your daughter will not outgrow it nor will it go away but early treatment/intervention will result in an excellent prognosis. The readings I suggested should give you some idea on how best to handle your daughter and her fears/anxieties; if this is not sufficient, then ask for a referral to a medical specialist with experience in anxiety issues. The key is always to "lessen the anxiety" and that is where many parents require professional help - each child is different and responds differently to intervention and/or therapy.
If it is any consolation, our child was far more severe in her anxiety at two years of age than your daughter, and today if you met her, you would not suspect there was ever an issue with anxiety. She is now a teenager. If you feel that I might be of more help, please write - either on this site or private message. I wish you the best ....