20 amp breaker keeps tripping...?

I know it's overloaded because I recently upgraded the breaker from 15amp to 20amp. The aluminum wire going in to the 15 was totally fried. Now the 20 is starting to constantly trip. I have four spots on the panel that are unused. Can I re-route the wiring on the overloaded breaker to the un-used breakers? Can I DIY this or do I need a pro? Bottom line - how do I get this done cheaply?