I have two badly infected ingrown toenails, should I go see a foot doctor?

Dr. Chuba. Gave the best advice you could get. Don't even try to mess with these yourself, especially since they're infected. The procedure to fix these is simple, fast and painless. You'll probably also need a course of antibiotics. Don't wait.
Podiatrist. You should see toe podiatrist immediately for evaluation.
Yes. Ingrown toenails typically do not resolve on there own without treatment. Save your money on over the counter remedies.