What ever you do, do it soon. Riding with questionable steering/stability is plane wrong.

A visit to your LBS should give you far more info then any one on the internet can. Yes, among the half dozen "answers" there is likely to be the one that is going on but some one still needs to figure out which of the possibilities is really going on. The LBS should be willing to take 5 minutes to look at and diagnose, then talk to you about corrective action, without charging you. Don't expect the shop to tell you how to fix the problems, that's how they get paid.

I like to do the easy stuff first. Air pressure, are things that spin (wheel, fork bearings) moving freely without slop or looseness, are things that need to be tight still tight (stem, bars, seat), doest the front wheel look to be in line with the fork and the rest of the bike and the rear end of the bike need a look at too. If the bike has suspension then that system's condition needs looking at. All this takes only a few minutes if done by an experienced eye. Now the fix might take much longer for all one knows at this point, but information is the first step to figuring out your problems.

Do get back to us with your findings. Andy.