Brought this philodendron (pretty sure it's a Black Cardinal) home earlier this past week and it wasn't wilting, but it was bone dry, so I gave it a little water (slightly warm as per instructions, and had been sitting out). It still seemed pretty dry a few days on and still wilting (As of this morning, began developing black stripes/patches with yellow edges) so I gave it some more water earlier today. It continues to get worse.

I'm worried if I should repot it into a mix with some perlite since the soil from the store seems very loamy, or if I overwatered it, or if this is a fungal infection and I should be cutting these leaves before they spread to the plant. If I overwatered it, can I just let it be to dry out or should I repot it into a dry mix, the sooner the better? I really don't want to lose this guy, never cared for one of these before, but I'm at a loss for what to do. Please help me identify this and if you have any solutions, I am welcome to them.

It does look like a Black Cardinal.
I agree the soil looks like it would stay too boggy. I would pull it out and look at the roots. If they look healthy, repot it onto fresh mix that is chunkier and better draining. If there are dead roots, trim them, but don't trim any good ones. Don't try are remove every bit of old soil, and don't wash the roots. If they are already compromised, that will only make it worse.
Repot it into a container just large enough to hold the root system plus about an inch all the way around.
These large growing self heading Philos can stand to dry out a bit between waterings. But not 'bone' dry. The water needs to drain quickly. It may have seemed bone dry on the top, but it could be boggy at the bottom. Make certain the container has lots of good holes.
I personally would cut off that leaf. It won't recover, it will just deteriorate.

Thank you @Gina1960 . Asides the repotting, is there any treatment I should do in case of an infection, or is this just a stress response? I have some perlite, as well as pebbles. Will either of those help the soil mixture?

You could spray the plant with a fungicide as a preventative, but if it does have issue with the roots, and you correct that, it should correct the problem. If you do use a fungicide, be sure to choose a systemic one, not a surface acting only one.
You can use perlite and pebbles, you can also use chopped up styrofoam, bagged orchid bark, pumice, aliflor, chopped raw nut shells, whatever is common where you live