Is liposuction the best way to deal with my Inner thigh chub rub?

If you are only 20 and you don't have a history of significant weight fluctuations, you are likely a good candidate for medial thigh liposuction to address this fullness (assuming the fullness is fat). Any existing excess skin could potentially become more lax with liposuction alone. 
If you are having skin tearing, I would certainly meet with a board certified plastic surgeon to discuss your options. The advantage of liposuction is that you have a smaller incision and a shorter recovery than that associated with a medial thigh lift. 

Best of luck!

Yes, liposuction would be the best option to give you an inner thigh gap and prevent rubbing.  The fact that you are young and athletic means you should have an excellent result.