Hopefully this thread won't be a negative pile on, but probably that is inevitable.
Basically, if you wanted to work in a nursing home you're going to have to get a covid vaccine. The only reason that they would let you work there without one is out of desperation for a warm body.
I personally am not super into a million vaccines, but even I got the covid vaccine. Let me ask you this question, do you drink soda pop? We know for a fact that soda pop is detrimental to the health. I personally don't believe hand washing is the number one preventative to disease. I think it is eating a healthy balanced diet, having a lot of physical activity in your life, and getting adequate sleep are stronger factors in staying healthy.
I see people adamantly against covid vaccine who are very careless with other aspects of their health. I think that is because they are distrustful of the government actions, the pharmaceutical companies, and probably ideological agendas surrounding this covid pandemic. I see the same hypocrisy on the other side of the fence as well.
If you want to continue your nursing career I advise you to get the covid vaccine. If I were younger I would probably get out of nursing and pursue another career choice. There are many opportunities to work from home now which sounds like it might suit you. The whole healthcare field has gotten pretty intense since this pandemic. I advise you to seek another line of work.