Scott, the very first thing you've got to do is determine the cause of the swelling. If no external punctures or abrasions are in evidence, then the problem is likely coming from inside the mouth. In that case, it may be that Louie has an abscessed tooth. And if that's the case, all of the penicillin in the world will only delay the inevitable. That being the need to remove the tooth. If left untreated, the abscess can spread to the adjoining teeth as well. This can and often does lead to the untimely demise of the cat thus afflicted.
A trip to the vet may be in the very near future for you and Louie, I think. But, he is young and very much worth saving a second time.
One question I have: How trusting of you is Louie? Can you pretty much handle him as you please? Or is he wild as a March hare when it comes to poking and prodding him? In other words, will he allow you to open his mouth easily and look inside? Maybe even use a Popsicle stick to press gently against his gum line to see if there are any especially tender places? [you'd know right away if there is, just by Louie's reaction.
] If he won't let you do any of that, then it's best to let the pro's handle it. Abscesses are no laughing matter for human or cat!
Another thought/concern I have is that you mentioned you thought that it could be a cyst. You might be able to determine that somewhat by palpating the area of swelling. Again, this is if there are no outward signs of puncture or abrasion type wounds.
Gently try to manipulate the area of swelling between thumb and forefinger. If it is a cyst, it will feel as though it is a part of his cheek tissues and not the gum. It will also feel as though it is sort of floating around in the cheek tissues, where as an abscessed tooth would be almost undetectable from the outside in its early stages. Oh yeah. Another way to determine: Check kitty's breath! If it smells rotten, then you likely have a puss with an abscess on your hands. If not,
Good luck with Louie, Scott. I hope that little bit of info helps and that your little fella is on the road to recovery soon.
Please keep us posted! And yes, been there, done that, got the T-shirt!