First off, let me Welcome you to Pet Talk.

Please bring your cat to see a vet to make sure this isn't anything serious.

We adopted a 7 month old kitten, that we didn't notice until a few weeks later, had red gums and bad breath. To make a long story short, he had about 3-4 vet appointments, different types of medication, blood tests and in the end, and many $$$ later, had to be put to sleep at the young age of 1 year. It was due to a severe bacterial infection that unfortunately was too late to treat as it had already started to attack his other organs.
But Scooter didn't just have red gums, his whole mouth was red.

I'm not trying to scare you here. I just wanted to let you know, not to wait too long before seeing a vet about this.

Good luck and please keep us updated on your cat.
Hope all goes well for him.