Ok Wracko, I have some time at the office and decided to try and explain to you what can help you. I just asked my Chiro. Having a proper evaluation is definately advised, but that being said, and knowing nothing about you, he gave me a generalized plan of approach for someone like yourself.
He told me you might want to do is Foam Roll/Stretch Illiopsaos, rectus femoris. stregthen tranverse abdominis (TVA) Internal oblique and Glutes. avoid loading the spine through back squats of course However, front squats are not as bad because it doesn't directly load the spine. go back to the basics and start there.
You might have what they call a lower cross syndrome? In which the imbalance form an X through your lower body.
So what you want to do is strengthen the top (abs, TVA, internal stabilizers), and bottom (glutes)
Stretch top (low back) and bottom (quads, hip flexor) X
I would throw in some muscle activation exercises. like hip abductions with a theraband, and practice the drawing in maneuver for pelvic stability. Locking in your neutral pelvic postion (neutral spine). Have the Physio help you find that postion and give you exercises that force you to try and keep that postion you just created. This is challenging if you perform it correctly. It will also help work the intrinsic muscles of your "core".
"Bird dog" exercises are one of these exercises that look simple but in reality, if you do it correctly, will help you learn how to maintain and control neutral pelvis. A simple way to do this is get on all fours and practice arching and rounding your lower back. don't move your shoulders just your lower back. Find the middle of those two postions and move your opposing arm and leg. the trick is to be able to not drop your hips or arch your back when lifting your legs. of course if your feeling any pain when arching or rounding your back, stop and go just short of that distance. The main goal is to develop and maintain a neutral (new normal) postion of your pelvis.
You can also put a brommstick on your back and practice moving your opposite legs and arms without the broomstick falling off. You can practice parallel with the spine and horizontal. keep 3 points of contact (back of the head, mid thorasic, and tailbone with the broomstick without the broom lol) i teach this every day and it's hard to explain in writing. maybe go to youtube and watch it there.
99% of people do core exercises incorrectly. There's more to having a "strong core" than having a "great looking" 6 pack.
Keep us posted. Hope you get this resolved and back on track.