Car wants to drive its self?

My car has gotten to the point where it will be fine one minute and then want to go all over the road.It scares me sometimes,especially when it rains.Was thinking a sway bar link,bushing,etc may be the culprit.I glanced under the front of the car and didn't see anything.It's raining,so kind of hard to get under it.I hear what sounds like a rattle coming from under the right front of the car sometimes,and when it happens that's the side it goes too.Any suggestions as to what to start checking first? thanks

Have you done an alignment recently? Check for feathering on the front tires.

Check your tires for wear,tires with not much tread and water don,t go to gether,they won,t even track right on uneven highway.Check your ball joints and tire rod ends for wear,swaybar rubbers,rack and pinion for excessive play.
Bad tires or worn front end pieces the car will have a mind off it,s own,the bigger the tire the worst and check alignment.
This is very dangerous for you and other people, take care and have it checked.

A broken sway bar link wouldn't do what you described. It sounds like when things are getting scary that something is moving that shouldn't be. Check the front end bushings; control arms, rack bushings, etc. as well as the bolts and hardware securing them for damage/looseness. As mentioned earlier check tie-rods, ball joints, wheel bearings for play or sings of damage also.

Excessive toe out can cause the front end to wonder but it should be more consistent.