Well if you're the least bit worried about it, STOP MESSING WITH THE TILES!!!!
Asbestos removal can be time consuming and expensive. OR, you can chance spreading it around the house, breathing it in and possibly developing respiratory issues.
I'd do some serious reading before you continue with tile removal.
Personally, I'd get a pro involved. Last house I had a potential issue with, it cost me $50 for a same-day asbestos test and it turned out negative. A very well spent $50 in my book!