First of all, heat is not necessarily a good thing.
If there is any swelling at all, ice is what you need. Heat will constrict the blood vessels and cause more swelling and pain. Ice will reduce the swelling and is what you want if you are going to rest the area.
Heat is good if you are going to exercise the area. It will bring in more circulation for that and allow your muscles to stretch further, but don't do it if you're not going to be moving around! A chiropractor may introduce heat to loosen you up for adjustment.
A chiropractor is a good idea. They will take x-rays and make adjustments and provide therapy to make sure the bones are in good working order, but it is up to your body to heal the damaged tissue or calm the muscles that are spasming. They just make it easier for your body to do its thing and provide as much movement in the joints as is possible.
If a disc is ruptured or bulging, or a nerve is pinched, or tendons are torn, etc. then a chiropractor will not be able to help you much. If you were in an auto accident or suspect something severe you will need to see a doctor, preferrably an orthopedist. In order to see what's going on, they will need to perform an MRI.
I was rear-ended last week so I'm going through this whole ordeal right now

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