So can the problem be solved with a new, higher AMP breaker if the wires are not messed up in the box?
NO, all this will do is let the problem get worse before the breaker blows. it's probably something stupid. like holding the wire up by driving a nail through it.
I'd
SWITCH THE BREAKER TO OFF
then remove the switch and put wire nuts on the ends of the wires running to the breaker box.
then switch the breaker on
if it blows then you have a problem in the wires to the box.
if not
SWITCH THE BREAKER TO OFF
then put the switch back in but don't conect the wires he put in leading to the fan.
then turn on the breaker and move the switch on/off.
if the breaker blows either when you switch it on or when you move the switch, you have a bad switch, replace it, then repeat these steps.
if not
SWITCH THE BREAKER TO OFF
and connect the new wires, take the tape off the end of them and replace it with wire nuts(more reliable than tape)
then switch the breaker,
if it blows he's damaged the wires and they are shorting
replace them with a fresh run of wire, you can tape the new wires to the old and pull the new in while you pull the old out.
hook up the new wire and repeat.
if you've made it this far the next step would be to hook the fan back up and see what happens.
the only really hard part of electrical (after you know the basics) is making sure you use the right guage wire. when in doubt bigger is better.
also always SWITCH THE BREAKER TO OFF. if you are the only one home fine otherwise tape over the breaker in the off position, or if you have children around who are old enough to throw breakers put somebody to guard the box so you aren't suprised by a live wire.
also never up the amps of a breaker or fuse(or god forbid do that stupid penny in the fuse trick) to solve the problem. the amperage of the breaker is set by the size of the wire coming from it. if you up breaker amperage without changing out the wire you will allow the breaker to give the wire more amperage than it can handle and possibly burn down your house.