With $10 whatever game you decide to play and whatever limit, sooner or later you will bust your bankroll.
The higher the buyin the faster the bankroll bust comes. The lower the buyin the slower it will happen. But I believe it will happen nevertheless.
Unless you have already the skills and you have the patience cause it gonna be a long tough grind and variance happens to the best of the best, especially in micro stakes. I would just deposit some more and try my chances with a mtt since I know I suck at cash games. Or at least play some freerolls so I can afford it.