why didn't gene do anything to help phineas after his second accident

The boys, including Gene, actually have the presence of mind to call the wrestling coach for first aid. Moving Finny at this point could make matters worse. I don't think there was any underlying emotional baggage that held Gene back when Finny crashed on the stairs.

He doesn't feel worthy to help him. He feels he has not been a good friend to Finny, and he feels guilty for all the pain he has brought him. He allows another boy to wrap a blanket around Finny, and then tells us "I would have liked very much to have done that myself; it would have meant a lot to me. But Phineas might begin to curse me with every word he knew, he might lose his head completely, he would certainly be worse off for it. So I kept out of the way."