[gbrhaz]

Your body will always compensate to overcome weaknesses. It sounds like your lower back has been taking the strain because the rest of your core (abs and glutes in this case) weren't up to it.

Normally planks are the best solution to this, including side-planks. They may be a bit too much for you though, it depends how bad the pain is, and how poor your glute activation is. Do you have any Anterior Pelvic Tilt (APT)?

Extremely light yoga might be a good thing to start with, as others have said. Childs pose would be good to do. Also Cat-Cow (Cat-Camel is another name).

As you sit at a desk all day (I assume) you'll be tight along the front (hip flexors, quads mainly), and your posterior will be weak/inactive (glutes, hamstrings). You need to work on fixing those.

Honestly though, you're going to want to see an experienced physiotherapist who can examine you and give you exercises which are good for your current situation. Any advice from anyone on the internet - no matter how experienced - should be taken with a pinch of salt, purely because we can only speculate.