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Indeed yes. It's called Side Loading, and requires you find (on the internet) the BAR file you desire (or, if you have the ability, convert APKs to BAR) and, via the DDPB installer app (for PC), side-load those to your BB10 device (PlayBook as well, btw). I have several side-loaded apps, and it's wonderful (though I do wish the devs would write some of my favorites natively for BB10).
Occam's Razor nearly always applies when troubleshooting technology issues!
If anyone has been helpful to you, please show your appreciation by clicking the button inside of their post. Please click here and read, along with the threads to which it links, for helpful information to guide you as you proceed. I always recommend that you treat your BlackBerry like any other computing device, including using a regular backup schedule...click here for an article with instructions.