GFI's are not designed to protect from overcurrent conditions
. They are strictly for ground faults. If you were drawing too much current, you should have tripped the breaker. From the way you describe it, it sounds like the power comes into your GFI then to outlet one then two. Since one has an issue, two stopped working as well but the GFI which is first in line is working fine. (Or you might not have the right idea on how they are wired.)
1) Turn the breaker off
2) Use a voltmeter to verify the power is off at all three outlets. This is not hard, but it is very important to verify the circuit is dead before you mess with the wiring.
3) Replace the damaged outlet.
4) Turn the breaker back on and check for power with your voltmeter.
Keep an eye on that outlet when you use a high load like the hair dryer just to be sure everything is back in order.