Depends what stage of the healing process, and how bad it looks. I don't come in contact with ingrown hairs enough, to distinguish if it is an STI or not. I tend to side on caution. (My shave schedule is set up purposely to avoid ingrown hairs, so it is rare I expierience them.)
Now that I think of it, I did see someone who had an ingrown hair situation. He let me know in advance so I wasn't alarmed, and we covered it with a bandaid to avoid friction irritating his wound. And I just realized it also protected him from my juices by creating that bandaid barrier as well.
I would think an ingrown hair has it's own look compared to STIs, I just haven't been exposed to questionable wounds thankfully.