violent shaking wont be cause by a balance problem at 45 mph. you may have a bent wheel, or a separated tire. ive had bad axles in my civic before and they would shimmy the front of the car so bad you thought a wheel was falling off, but it would only shake under acceleration.

my reccomendation, is to go to an alignment shop, have them inspect the tires and the front end. tell them you want a balance (like 5 bucks a wheel). a balance check will tell you if you have a bent rim. good luck