If you are experiencing some social challenges and anxiety that you would like help with, you should certainly seek some professional support from a licensed psychologist. In addition, your children will need support in the development of their social sk, and you will certainly be in a better position to provide social opportunities for them if you can overcome some of the social difficulties that you are experiencing.
Google DSM IV and look at the diagnostic criteria for Aspergers. You have to have difficulties in all the areas mentioned to get a diagnosis.
I would also consider whether a formal diagnosis will be a positive thing for you. Try to find out if it will affect your insurance premiums etc, or it may give you access to certain benefits you don't currently qualify for.
As well as difficulties with social interaction those on the spectrum usually have difficulties with language and may take things very literally and not understand certain types of humour such as sarcasm. With Aspergers there is also usually interests and obsessions that are not usually typical. There is also alot of anxiety as well as difficulties with 'theory of mind' and imagination or predicting outcomes etc.
As you are interested and willing to improve your social skills there is every chance that you will be successful. But that may mean that you have to rote learn a mental list/procedure to go through to try to help you at times when things are not obvious to you.
If you think a diagnosis would be useful to you, then you could talk with the professionals involved with your children and tell them you think that you too may be on the spectrum and would like to be assessed and ask them how you would go about it in your area.
It maybe that you have some traits, but not enough to get a formal diagnosis. I have some sensory issues, auditory processing problems and tend to be quite solitary - although I can enjoy myself in large social settings if I'm in the mood for it. I think it is quite common for traits of autism/aspergers to be in family members when there is a child with a full diagnosis.
But, although you may struggle with some things, you are in an ideal position to understand how your children are perceiving things and what kinds of supports would be helpful.
I think it is brilliant that more and more adults on the spectrum are beginning to work in schools/adult employment to help others understand what is behind the difficulties. And as well as causing you some difficulties, autism/aspergers also has some very positive aspects to it eg. total concentration and endurance in areas of interest, original approaches to problem solving etc.
If you don't think a formal diagnosis would be helpful, it might still be useful when seeking help or advice about your anxiety/panic attacks to mention that you have children on the spectrum and think you might have aspects of it as well. That should help professionals give you a more suitable approach to helping you with your difficulties as the basis of them may be completely different from other people who are not on the spectrum.