Hi, fellow female aspie here.

I've been lucky enough to have had professional help for my social anxiety and other issues, however, I must stress that it's 99% of what you do outside of therapy that is important (obviously).
There is only really one way to overcome anxiety - exposure and practice. The two most painful things!
For me, when my social anxiety was really affecting me, i set myself goals which i had to complete. It started of with 'simple' tasks like smiling at someone or saying hello (even having a conversation with family) and then progressed to more difficult tasks such as meeting new people or joining clubs.
These are just examples and I know they seem daunting, but try to pick something that is just about managable to you - as far as anxiety - and do it!
It will take a while, but it does work. Practicing social skills will help you improve them. As far as confidence goes, doing things which you find difficult is always a good boost. (I went to a concert on my own a few weeks ago)
If you struggle with eye contact, again, practice is the key. It took me many years to (only slightly )improve it, i've sort of come to terms with accepting the way I am and not caring too much about how others view me with my awkward body language.
If you get on well with your family, try out your 'practice' on them. I know it sounds stupid, but you can practice engaging in eye contact or making small talk without worrying too much about feeling stupid if it goes wrong.
Have you thought about getting a job which doesn't require too much interaction? Maybe with animals or 'behind the scenes'?
I hope things get easier for you