Thankyou for the help
I cannot diagnose the actual problem from the internet based on your description so I can’t estimate the cost either.
It IS a safety concern. You SHOULD get it checked out by a pro.
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I’d guess engine is misfiring, but could be a tire problem as well. Does the sound change when shifting to neutral & coasting?
If steering feels like it is locking up, that must be addressed asap by your shop. I expect you already know that’s a definite safety issue.