I too struggle with social anxiety, OP, but to a much lesser degree than you. However, if my SA ever started dictating what kind of jobs I did or did not feel comfortable doing, I would know it was an issue. If your SA is impeding on your ability to get a job, or work certain kind of jobs, it is a big problem and you need to seek appropriate treatment. I know it can be hard when you're a nanny and don't have health coverage - I'm actually Canadian but therapy is not covered. I have paid out of pocket in the past to see a counsellor and would not hesitate to do so again if I needed to.
I'm not trying to get down on you or criticize you at all, because I understand how hard it is. Some anxiety can be managed on your own, but some cannot. I recently started seeing a therapist again because I started having anxiety attacks every time I worked out with my personal trainer (which was super embarrassing, but a huge signal to me that I was not managing that aspect of my anxiety well enough on my own). You said "the panic inside is so strong" you avoid interactions. The last thing you want is to start having anxiety attacks while working, and feeling overwhelmingly panicked inside is the last step for me before I start expressing it as an anxiety attack.
I totally understand preferring the company of kids to adults. I love my toddler charge and love hanging out with her all day. Thankfully, her parents are as socially awkward as I so I feel pretty comfortable around them. I've definitely felt intimidated by and shy around parents before. But the bottom line is that to be a good nanny, you need to be able to deal with adults: both for things like scheduling play dates and lessons, but also to model things like talking to strangers and being polite to cashiers, etc. Frankly, and I'm not saying this to be hurtful, if I were ever to hire a nanny and knew they struggled with anxiety (or any other medical condition that could impact their ability to work for me) and weren't actively seeking treatment, I would question their judgment. This doesn't sound like a great quality of life for you, OP, and you definitely deserve more. Even if you are the best damn nanny in the world, you should have more options than nanny and night shift security guard.
I guess my bottom line is that it sounds like your anxiety is affecting your quality of life, which means that it's time to deal with it instead of resigning yourself to a life of avoiding adult interactions. Things can be much better

Good luck!