even a timid tame cat like I have will fight tooth and nails to stay out of that carrier, and they know when it's time for a trip to the vet.
You need to be patient for a bit and keep feeding her, that's how you gain their trust. You really should get her to the vet. We have 2 outside cats, one is pretty tame but the other is iffy. Glad we got them both to the vet, we had them neutered and found out that the one had feline leukemia, I think that was it. So since the 2 outside cats got along we didn't listen to the vet to have the cat put down. He has been living the life of Riley for 3 years since that advice.
I suggest throwing a towel over the cat when you are ready to get it into the carrier and push towel and cat both into the carrier and have the carrier ready, the quicker it happens the better. I screwed up on the 1 outside cat when I went to push him into the carrier he stuck out his back legs and pushed the carrier off the porch.
Patience is a virtue. Oh, a 3rd cat showed up outside and I can't get near him/her, but I feed him away from the other 2 outside cats. Don't believe this cat will ever come close to me, but I keep trying.