Hi - it sounds like you may have some issues with the discs in your back and possibly other structures in that area.
Having suffered from severe back pain for over 11 years - mine started after a four day drive - having driven for 12 hours each day there and then the same drive back!! Sitting down driving long distances puts a lot of strain on your back and will likely highlight any weaknesses there.
You really need a diagnosis and most likely a CT or MRI scan would be the most appropriate. With long term back pain - and no diagnosis, there are serious complications that can occur - though not always. Seriously though, once you have a scan - your doctor can diagnose the cause. Disc issues/back pain does not always require surgery so don't let that put you off. Once you know what exactly is wrong - you can start to treat it.
Mind you - some people do have severe back pain with no evidence of injury on scans and/or xrays and the pain is no less real. However, at the other end of the spectrum - if something is for example - is compressing your spinal cord, then that may need urgent treatment.
If your pain is not a regular thing and you are looking at pain relief - then ice packs can help more than heat on occasion, and hydrotherapy via a physio. Caution though - a good physio would want a scan before treating to ensure they know what to treat.
Hope this helps a bit - at least
An MRI is probably the best way to see what's going on, but you could try a treatment called myofacial release, which is a massage that works on your whole spinal area and thoracic joints. Some chiropractors offer this service.
Good luck!