It's simple: you have a weak back. So strengthen it. The first thing to do is start a program to fix it. Since you're starting at the bottom, buy yourself a copy of Core Advantage, start at the beginning and over the course of a year, work your way through it. Give yourself a whole year and keep at it, even though your back will start getting better in a month.

Once your core is functional again, you might want to expand on it by doing some upper body work at a gym.

You're experiencing muscle spasms in your back. Back in the day, doctors would prescribe rest and muscle relaxants. Finally some bright person figured out that a weak back needs to be worked, not rested. When I had a similar problem, I worked my back pretty good, until it started to hurt, then I'd rest it for a day, then work it again. After a while I could work it every day.

I doubt very much that it's a bike fit problem. If your core is strong, fit becomes largely irrelevant.