Sounds like you are going to have an exhaust leak in the system. The deep water could have gotten in the system and blown a hole, or the exhaust getting "caught" on something while getting the oil changed could have created a leak. With the engine running, cover the tail pipe outlet with a heavy rag for no more than 5 or so seconds. Have someone look underneath and try to pinpoint where exhaust is leaking.
If it is a leak.
Will i damage the car if i continue to drive and dont fix the problem?
How much is the fix?
It will not do damage to anything else right away. Over time however, yes, damage can be done. I wouldn't suggest driving it too long like this. As for how much- there's no way to tell until you find where the leak is. If its a hole in a pipe, the pipe will need to be replaced. If it is a broken "seam" from being "caught" on something, maybe just a new gasket and nut/bolts may fix it. If its a hairline crack leak, it may be possible to weld a patch over it.