I found a stray cat about a week ago and everything was fine until she started to get lesions around her neck and I was wondering if I could go to the shelter to get her examined?

Shelters are just for that when you're ready to give them up. Go to the one on Sepulveda west Los Angeles. Plus they're are a no kill shelter. They are well funded.

If you aren't planning on surrendering it to the shelter they can't help. There are animal rescues that can help but your best bet is taking it to the vet.