the anti-cheat has a pretty good track record against false positives... you sure you didn't have any software running along-side the game that could have been misconstrued as an injection tool or anything?
Even so, creating another account to circumvent a ban is a no no... your best bet is to wait out the ban until it's over because the next one i think is permanent.
In the mean time, figuring out what triggered the anti-cheat will be important so you don't get that third strike.