Stray Cat Advice

Looking for advice on places / organizations that will take in stray cats. We live in Huntersville and Thursday night this cat showed up outside our house. She’s very sweet, affectionate and socialized but is pretty skinny. We think someone dumped her or possibly she’s a lost pet. We posted on the local lost animals FB page, took her in and checked for a microchip, filled out a found pet report and are unsure what to do next. We have a cat already and are unable to adopt her. We’re not sure if she’s fixed or has any vaccines. It seems like the Humane Society only takes former pet cats with a medical record? We drove her to the county Animal Care and Control shelter this morning but were turned away because she’s no longer a kitten. They told us the only option was to call 311 and have her picked up or drive her somewhere else and dump her (seems extremely irresponsible). She’s a great cat and we really want her to have the chance with people that will take care of her. Are there any local groups that will take in strays?