the first mechanic was probably right. you need front end work. BUT, when you do front end work your car needs a realignment. so… yes, you need an alignment, but the guy probably didn’t go into all the junk you needed also.
since you found a mechanic to do the work, and has quoted you the problem, and the price, (which doesn’t seem too high) you could try him. or, go back to the first guy and ASK him what specifically is wrong, and how much.
as far as your question about safety. well now that the storm has passed, and the roads should be clear it would probably be OK to drive. BUT… like winning the lottery; “Hey you never know!”