How does a PT who understands pain react to an “injury” while working out? Part 1

As a Physical Therapist who understands pain, here’s how I reacted when I hurt my back while deadlifting on Monday:
I was deadlifting about 80% of my 1 repetition max, which is a weight I lift often. For whatever reason, by the second set, each rep gave me more and more soreness and pain in my left low back. (This is when I would tell someone to stop). On the 3rd set, I got a really intense, sharp pain, 9/10 pain, in my left low back after the 1st rep. I felt a snap. I was actually limping while walking. I limped over to the turf in the gym and laid down to experiment.
I did some mobility exercises on the floor. And I tried doing a full bridge, which hurt a lot. But I was able to do every exercise with at least partial range of motion, and I did them for like 5-7 min total or so. Getting up from laying down hurt, but not as bad, so it felt better. I went on with my workout, still in pain, limped for a few steps but that went away. I was originally planning on doing pull ups after deadlifting, but decided it wasn’t the best idea. I moved on to the lat pull downs I usually do but with a lighter weight, a weight that I was comfortable doing. I do them a lot, about 3 sets to failure with wide grip row bar and 3 sets to failure with a regular lat pull down bar. Then did 4 types of arm (bis/tris) exercises, 3 of which I was standing for. With all of these exercises, I did a lower weight than I usually do. I did a weight that I was comfortable with. The pain got better and better as I went through my routine. As I was leaving, the bridge was pain free and getting up from the floor hurt a lot less. I was good enough to be able to go to Brazilian jiu jitsu training a couple hours after hurting my back. I did have some low back pain while training but it wasn’t too bad.
The next day, I was pain free and went to go treat patients with low back pain. I went to the gym after to do chest and shoulders and went to squat. I tried to do a full ass to grass squat with 50% of my 1 rep max, but that hurt my low back, so I did a box squat with that weight which felt good. Every other exercise was normal for chest and shoulders
2 days later went back to deadlifting with 60% of 1 rep max with no pain, did pull ups after that and had a solid gym sesh doing back and arms.