Is it possible to alleviate knee pain with exercise?

I am a woman in my 50s. I started doing lower body exercises at the gym, but my knees started to hurt. It’s okay when I walk or do other activities, but it hurts when I sit down or stand up. It also hurts when I sit cross-legged on the floor, so I can't do it. I am worried whether I am exercising incorrectly or if my joints are degenerating now. I am delaying going to the hospital because I am afraid, but will it get better on its own?