I currently own an Epiphone Supernova and a Mesa Boogie Studio .22. I can't seem to get anywhere near the sample settings for the amp without terrible feedback. I think it might be a broken tube in the amp...but I can't be sure... any suggestions?

Go to your local guitar shop.
Ask them to check it out, they usually do that
for free.
OR you can take it apart and check the tubes(not recommended).
I guess if a tube is broken you'll have to go to the guitarshop anyway so...
OR you can take it apart and change it yourself(not recommended).

Kick out the jams.

If you don't know what you're doing...or in other words..."When in doubt" take it to the shop. You don't want to screw it up worse than it already is. Congradulations for picking an expensive hobby!