The front part of my foot hurts after I stepped in a hole. The pain won't go away, but I can walk on my foot. It just throbs and hurts and there is no swelling. What should I do?

How long hurting? It sounds like a soft tissue injury, which will heal with time, and limited weight bearing. Ice alternating with heat may also help. If the pain persists more than two weeks, it should be evaluated by a foot doctor (podiatrist) or an orthopedist, preferably one specializing in foot/ankle. The possibility of a stress fracture with the injury you describe is a possibility.
Trauma. Hi-- when was the injury / hole incident? If it was longer than 6-8 weeks ago then you probably should get an x-ray. Fractures / broken bones (same thing) heal in 8 - 10 weeks but the foot can be painful for several months. You can walk on broken bones- that is not always a determining factor.
See dr. It may need imaging if indicated after exam . Dr can help with proper diagnosis and pain management . You may have a small fracture.
Maybe sprain or bone. You may have sprained your forefoot or may have sustained a bone bruise or tendon trauma. Try icing your forefoot 10 minutes several times daily for relief. You could also take 2 advil (ibuprofen) twice daily as well.