How can I revert my Macbook Air back to Mountain Lion?

I got my Macbook Air for Christmas in 2012, so it's only a little over a year old. It came with Mountain Lion, and it's been fine, until I updated it to Mavericks. Well, it was alright for a little bit, until the past two days, it has frozen on me for absolutely no reason at all twice. I wasn't running a lot of programs or anything, my hard drive space was fine, my battery was fine, and I've taken good care of it (never spilt anything on it, dropped or banged it). When it froze, the keyboard and cursor didn't respond, it wouldn't go into sleep mode and the sound skipped. All I could do was hold the power button until it shut off. So I was doing research on it and I think the reason is Mavericks. So I backed up my important things onto a separate drive, and I did the restart with command+r and I erased the hard drive completely. But now the only option for installing is reinstalling Mavericks, which I don't want to do because I'll be brought back to square one. My brother has a disc for Snow Leopard, but apparently you shouldn't downgrade a computer to a system software older than the one it came with...does this mean I have to buy Mountain Lion now or something? I don't have any backups in Time Machine (which is stupid of me). My mom has a Macbook Pro with Lion, but I don't know if I can do anything with that (unless it came with a CD, which I don't think it did, and besides it's still an older version). Am I just stuck with Mavericks then? I wish I never upgraded...unless the freezing is related to something else?