I can hopefully give you a couple of things to try - speaking as a very dysfunctional person that's had to learn to fix themselves!!
I don't buy your PT's reasoning (I got told this all the time). A well functionally body can cope with pretty much whatever you throw at it provided you build up to it gradually. The PT's job is to fix any unbalances - not just tell you to cut back on training. That's a cop out.
Trigger points in the QL can cause pain. It's pretty easy to resolve with self-massage:
However, most of the time, if a muscle is tight and forming trigger points it's for a reason. It usually means there's something wrong elsewhere.
I've become a big fan of NeuroKinetic Therapy (if you're on fb look them up and follow their page as they regularly post up really useful stuff). Their view is that muscles tend to get tight and painful because another muscle elsewhere is inhibited. You can stretch the tight muscle until the cows come home - it'll stay tight. But find the inhibited muscle and re-activate it and the tight muscle will let go. I found this video from NKT that talks about a possible scenario where the QL is tight and painful because it's compensating for an inhibited Traverse Abdominis and Psoas.
This is of course just one scenario that could lead to QL tightness - there will be others.
If you can figure out what's inhibited then it's a very quick fix as it's a neural problem rather than a strength problem. You just need to fire up the right firing sequences and everything resets itself. A good approach is to find out all the synergists of the QL and test them for weakness. Test antagonists too. The problem usually isn't where you feel the pain.
Just some stuff that might give you some clues. Good luck