I have had that before, as a combination of using the mouse and playing with tensed arms and stiff wrists.
Right now, to protect my weaker right wrist, I wear a guard (thumb and wrist stabiliser) while typing at the computer.
Just curious, which Hanon exercise were you playing? I know that some of them require huge stretches, which might have strained your thumb and wrist.
If it hurts, please rest. You might have simply overstretched. Stop playing what hurts you, as it cannot do you anymore good. Tell your family that you are hurting. Your teacher would need to know as well, if he/she is open-minded enough to understand that you are not giving excuses.
If the pain does not go away even after resting the hand, go to a doctor. I went to one, and was diagnosed as simply fatigue from overuse of my hands. The pain went away with rest and massage

But the same pain comes back when I work for too long at the computer, and I have to resume the massage.
In the meantime, do read up on Repetitive Stress/Strain Injury (RSI).
http://en.wikipedia.org/wiki/Repetitive_strain_injuryYou can type RSI in google and find out more.
Don't ignore your condition till it is too late. I have had a keyboard teacher who suddenly could not control her hands one day while conducting a class. Her right hand could not even turn a door knob when it happened. She has ignored the pain in her wrist for a very long time, and it has become so serious that she could not play the keyboard for some time. If she sought treatment earlier, it could have been as easy as ample rest and some massage to release the tension.
EDIT: Just in case you want to know what kind of guard I am using, this is the one:
http://redirect.futuro.com/products/show/845#It offers some support, but is not a cure.