Thanks for the comments. :(
Whether it is separation anxiety or just anxiety, I believe you. Our elder granddaughter suffered anxiety from the moment she was born. The second granddaughter cried for five hours once when we babysat her (and she knew us well). Our elder granddaughter required a lot of help from professionals; our younger granddaughter was able to cope with support and patience from her family.
Advice - there's no easy answer. Just do what you have to do - if you must leave her, then do so, Where's her father - gradually someone else will need to help you but it will take time for this child to become comfortable with others. Just know that you are not alone and it will get better. If not, (after a couple of years or so), then you will need to contact your pediatrician for further advice. But for now, I might suggest you google the phrase "anxiety and toddlers" or "anxiety and babies" to see if there might be some information on the internet. So sorry - but this will take time and it is torture ...