My first batch - and fermentation stopped after two days..?

Airlock size is not going to affect your fermentation. Not sanitizing is not going to stop your fermentation. It's possible that attenuation is simply finished. It's also possible that it is continuing, depending on how airtight your fermenter is (isn't). Bubbles are not a particularly good quantitative indicator, and are a terrible indicator for a first batch. Wait a week and take a hydrometer reading. Then take another one 2-3 days later.

Read this while you're waiting...
www.howtobrew.com

Edit: the one thing I would make sure of in the meantime is that your wort is in the recommended temperature range for whatever yeast strain you're using.

 

Relax, Don't worry, etc, etc, etc.
You don't mention the details of your brew - original gravity, expected final gravity, yeast status, temps, etc, but I would guess that major fermentation is about done. I still would leave it about another week and a half or so before even thinking about popping the top to check gravities. Do so then, then again another 2 or 3 days later. If it's the same at that point, then think about bottling.
If I had to guess, I'd say that major fast fermenting is over, but there's still some going on, plus the yeast are cleaning up after themselves.
As VikeMan said, airlock size itself doesn't have anything to do with fermentating, as long as it's preventing air from getting in.

 

Well, even if air is getting in, that's not going to stop fermentation.

 

Sounds like it's working fine. Vigorous fermentation often only lasts a couple days. Chillax and have a brew. It will come out fine. Leave it be for a couple weeks and brew another one in the meantime if you can.