When I was a kid, I once became ill and had to stay home from school. The doctor prescribed me some antibiotics to kill the germs, and his directions were to finish the bottle. After taking about half the bottle, I no longer felt sick, so I figured I must be healed. I stopped taking the antibiotics. A week later, I was sick all over again.
Just because the symptoms were gone, it didn't mean I was completely well yet. So, after the pain is gone, the hand may be in the final stages of healing, so continue to rest the hand a while to make sure it heals completely.
If you can type okay, I'd be curious to know which tendons you injured, and what it felt like. Also, what did your teacher say about it? Besides what's already been suggested, I can only add that seeing someone who specializes in injury-preventive technique may be helpful. That's what I've been doing.
It's important to let your hands and arms "breathe" when playing, especially on demanding works. Ever tried to hold your breath while lifting weights? It's not a good idea.
Taking little breaks not only helps to rest your body, but also helps you to understand and appreciate the music better. Musicians tend to work very obsessively. Sometimes in university practice rooms, I'd hear students having 2 hour practice sessions without a break, as if they were playing a single piece 2 hours in length! The brain gets fatigued and disoriented, because it gets conditioned to hearing sound; the music doesn't "stick out" anymore. Then you lose awareness over your playing.
I often would play like that. Then one day, after some tiring playing, I decided to rest, which I rarely did. I sat in front of the piano for a couple minutes, without playing. Not hearing myself play was actually shocking to me! I suddenly became aware of sounds that I didn't notice while I was playing. When I started playing again, I felt much better. By allowing myself to hear silence, I became much more aware of sound.
Anyway, this is largely a digression. Hope your hand heals soon.
- Saturn