I'd just like to clarify a few things ..
You raised a concern about getting fired ? Is this woman in a senior position to you ? If she's not then I can't honestly see a lot that would get you fired unless you do seriously blow up at her one day.
Have you got a supervisor ? If you have, what you are describing is work place bullying and you are well within your rights to have a word with your supervisor, explain the situation and if you're concerned about what she's saying being taken seriously you can always say look, I don't want to take any action about this but I wanted to query whether there are any concerns about the standard of my work etc. I'd also suggest asking them if there is any training/work place progression things available that you could take part in to boost your confidence in how you are doing at your job and your job security. (If it's a hospital would they consider training you up for care jobs ?)
Also are there any positive people that you get on with in your job ? Maybe try and work a bit more with them/take breaks with them so you don't have to be focused on this woman so much ??
I really hope the situation improves because I know I've left a job before due to bullying and the only way I got through it was by trying to make it as positive a step as I could so I felt like I was leaving because I chose to , not because they made me and I was going on to something much better.