What is wrong with my 2001 Dodge Neon?

In thw winter especially, my car will slam down after going over a bump. I was told this is the struts. I need to go on a 700 mile trip, but was also told not to go on highways with the car like that or they could snap & shoot through the bottom of the car, or I could swerve off the side of the road?? Also when it rains/snows, the right front side/tire squeals loudly?? Appreciate any advice. Thanks :)