Summarize:

Shaving over razor bumps will only irritate or tear them open, leaving them vulnerable to infection (and probably not removing much hair in the process). If you can, let the hair grow for a few days and see if it breaks out of the bumps on its own. It might itch, but breaking the bumps with your fingernails can lead to infection and scarring. Try to hold off as much as you can. Look for something that contains salicylic acid, glycolic acid, witch hazel, aloe, or any combination of these ingredients. Some of these products might come in a roller bottle that's designed to go directly on your skin, while others might require you to put the solution on a cotton ball and dab it on your skin. If you don't know what to buy, call your local waxing salon and ask what they recommend to their clients. You can probably purchase the product there as well, or look around online. Apply the solution to your skin at least once per day, if not more. Aim to do it when you get out of the shower, before your skin has sweat or anything else on it. If you suspect that you have infected ingrown hairs, try using an antibacterial cream on them each day. Bacitracin, Neosporin, and Polysporin are all possible topical treatments. Retinoids, derived from Vitamin A, can help smooth over skin and reduce the appearance of scars or marks left by razor bumps. You might need to see a doctor for a prescription. Do not use Retin-A if you're pregnant or breastfeeding. It can cause severe birth defects. Areas treated with Retin-A are more susceptible to sunburns. Cover up, or wear SPF 45 sunscreen. Don't use Retin-A on any areas where you plan to wax in the future. It can make the skin significantly weaker, leading to potential tearing during a waxing session. If your razor bumps persist for several weeks, and you haven't shaved again, consider booking an appointment with a dermatologist.
Let the hair grow out a bit before shaving again. Resist the urge to scratch the area. Use a product that's designed to treat razor bumps. Treat infection with aloe vera then lotion, to leave your skin clear and smooth. Treat scarring with Retin-A. See a dermatologist.