I'm not a doctor... but I'd say you probably did not do any damage (or
at least not accute damage) to your ear drum. If you did... you'd
probably have a lot of pain. Sounds like you just jammed a wax plug up
against the drum. As for those ear cleaning kits with the bulbs... I
have had limited results from them. 99% of the time they just make
things worse by filling my ears with the softening fluid and water that
won't seem to drain out... and it takes a good week for things to dry
out again. Basically... I'd say you have really only good solution... go
to an ENT or a GP who knows what they are doing and get them remove the
wax with a curette. The curette method (a curette is like a teeny tinny
little melon baller type instrument... they just pick the wax out
manually) is preferrable to the high pressure water/syringe method.

As for q-tips... I actually DO use them... but I used them (very
carefully... circular motion... no poking) on an almost daily basis...
and more so just to apply some polysporine to keep things nice and moist
and clean than to remove wax build-up. I think this daily ritual helps
stop the wax from building up in the first place. Once you have wax
build up though... a q-tip is almost certainly just going to act like a
'battering ram' and make things worse.