How to cure a deep cut?

i got a cut on my finger toe about 2 inches long and it's kinda deep cuz i see a flesh like popping out.gross. sorry to say.i got this wound yesterday as i was swimming in a rocky beach.and it wasn't rIy painful, I got off from the water and i put some "malunggay" on it so that it will stop bleeding. it kinda did. I got home and immediately washed off. it was so painful like heck. i used an antibacterial soap and dried it with a clean towel softly. and i carefully put some alcohol on it in a cotton.i grit my teeth (>.<) and then i put a gauze bandage. Was it okay? and i have to use shoes for school,it really sucks. it stings! i just have to bear it cuz i dont wanna wear slippers at school.so yeah.please help tell me how to maintain a good way to make my wound heal faster and be away of infections?thnks!