ok this ones easy
yep your ears are getting screwed
1st thing that you have to know is that sub woofers are more or less pointless for whoever is driving the car unless you drive a limo, hearse or reallly long station wagon (or a bus) simply because the wavelength of bass frequencies are so long, that you have to be a fair way away from the source to hear it properly. thats why the people outside ya car hear it louder/bassier than you do. coz of this, you cant get a real good idea of how loud it really is so you can really be screwing your ears.
the ringing in your ears (tinittus) means that you've done damage to your ears. that sound is actually your brain recalibrating with you ear to account for hearing loss. it has strange ways of fixing things but most common is to patch up the frequency you've notched out through blasting the shit out of it in one ear, with the sound coming through the other ear of the same frequency, (assuming that ear works in that region). but basically, if you hear it a lot, you're well and truly rootin ya ears which is a bad thing.
anyway hope that scares you away from subwoofer, and please tell me your bought a decent one, not a stupid ported one note bass sh*tjob from sony/alpine/pioneer etc. etc.
cheers,
from me
ohhhh and earplugs are usually a bad thing unless they are properly moulded to your ear + have inbuilt volume attenuating diaphragms. and they cost about $200 a pop depending on were you get em