My cat has a really swollen eye that she won't open. I tried getting her to and she flinched her head away. What can I do? Does she need to go to the vet? Is there anything I can do at home first?

Have you tried bathing it in warm water to see if that sooths it?
If it looks like there could be an infection use warm salt water.

I just dabbed a warm wet cotton pad on her eye lid and she ran away and didn't like it.

OMG, thank you for prompt reply. When I went back to her to apply the salt water solution her eye was a open a little so it looks like it's going to be OK. Man, that was a relief.