Lat pull-down translation to pull up?

I got to 3x9 on pull ups; Overhand, hollow body, full RoM, three minute rest breaks. Decided I’d add weight, lowest DB at my gym was 10 lb so put it between my feet and got to pulling.

Tore/sprained/pulled something in my left shoulder I think. Fairly minor. Was able to do my entire upper body workout afterwords, and leg day the next day without issue. Just hurts if I try to do pull ups or put that arm behind the back, like you’re getting arrested, and move the hand up my back.

Anyway.. long winded way of getting to today when I went to the gym again and tried doing lat pulldowns, landed on 115-130 lbs as my starting weight range for 3x9. I weigh 168 lbs atm, but am about 18% BF.

So, shoulders weren’t really entering the movement for lat pulldowns, but they were with pull ups. Can anyone shine some light on this, and the relationship between the two exercises?

Also any idea how I injured myself? Normally there’s some sort of physical pain that serves as a warning when I’m about to injure myself but in this case it was pretty abrupt. That or I was just super locked in and didn’t notice. Felt pretty weak that day for some reason so I think I was less ready for the extra weight due to that. Maybe I should start with a lower weight once it’s healed (I’ll go back to unweighted first).