Mild injury / should I slow down my progress even if I can handle the intensity.

[Wet Coast]

Quick Background
Prior to starting the Starting Strength program in April I have not worked out in a Gym for about 10 years, I have made my own workout equipment while working in camp and followed a redneck HIIT / Met Con type workout program. I haven't actually done anything other than a run or hill sprint for about 4 years since I started my own business. I have always had very physical jobs and a healthy appetite. I decided to get back to some form of training partially because I've been feeling creaky and beat up for a long time and partly because I was replacing my roof in march and my buddy catcalled me with "dad bod" as he was driving by.
I've been following the LP since April 17 but with a struggling company, 3 kids, etc. I have had to modify the schedule a little to deal with life. Because I can't always get either time to workout or enough rest I have broken the SSLP into the number of workouts for each section instead of going by the number of weeks. I just finished the first section that Rip says can last up to 3 weeks (9 workouts for me) Eating wise I basically jacked up the carbs and eat till I feel like I'm going to puke at least 1 time per day with a whey shake after my workouts . It has been going very well but I am finding that the weight particularly the deadlift is getting a little scary and I am starting to feel gravity pushing back a lot more.

Since April 17 in 9 workouts I have gone from
31yo
5'11.5 236lbs - 248lbs (25-27% BF ? Honestly don't know I have 4 abs if that helps never seen the other two no matter how much I lose, don't seem to be any fatter than a month ago)
Squat 235 - 305 5x3
Bench 135 (failed last rep) - 200 5x3 (I know I benched like a little girl but I have had a lot of rotator cuff issues from an old injury I guess I was weaker than I realized)
OHP (115-135) I didn't fully realize the layout of the program and missed the first several OHP days also press like an infant :-)
Dead 315-400 5x1 I screwed up and was doing 5x3 up to 385 dropping to 5x1 was a big help!

So my question is today pulling the 400 dead I was ok on power and probably could have done at least one more rep but halfway through I pulled something about 3 inches down from the bottom of my shoulder blade, dead center in the loin ( at least that's what it would be on a pig lo. I'm not sure what the name of the muscle isl) I finished the set but it feels like one of those things that is really going to feel like shit tomorrow. So my question would be am I better off dropping a bit of weight and working back up if I'm pushing that hard or should I just be less aggressive on adding weight? I haven't missed a rep other than the first day of bench press and with the exception of the deadlift I have mostly felt like I always have another rep or two in the tank. I have been throwing on some weight because it felt too easy (eg. 2 workouts ago I felt good and added 15 on the bench no problem) is that a bad idea should I just be patient and take smaller gains? I can't afford to be hurt badly because I would essentially starve and being self employed I don't have any real option other than to work through and injury.

Any input would be great, I know that since my next workout is the start of section 2 of SS I will start with a clean instead of a dead for workout 1 and that should give me a little recovery time and hopefully I will be at 100% after that.
Thanks
Nick
And a Serious thumbs up to Rip and his system since I walked into the gym I have hit new PR's every single workout which is super rewarding compared to just working out because you want to get in shape!

[Toasterleavings]

It's a long game. You can lift for decades. Injuries don't add weight to the bar.

Work up with pain as your guide. Don't push through an injury. If you can work around something, do that. Nothing wrong with taking a light day or week.

This is really good advice. Dont have to be here long to see quite a few people suffering injuries when they start to get strong. Dealing with those sensibly can get you past the teething problems into a more stable run of getting stronger. Probably a next stage where people get into more beastly territory and start ramping up the injury rate again, but deal with that when you get there.

Make sure your form is ok. Post some formchecks as a minimum or get a coach on board for a bit if it is feasible. Best of luck