"I felt a twinge/tweak/pop/thud/detonation at the start of my session, but I just pushed through....."
This ill-fated sentence is one of the main reasons I have a job.
If it hurts, don't do it. This applies to many things in life (dress shopping, public transport, vodka), but in particular to strength training.
Obviously you are putting your body under a lot of stress, and asking it do to horrendous things over and over again. Please see the definition of insanity which is repetition in something but expecting different results over time. Why oh why would you be able to push through an injury? Why would you train despite being in pain? Unless you are Wolverine do not do these things.
Pain is the last step of dysfunction. Say it with me -- PAIN IS THE LAST STEP OF DYSFUNCTION. Listen to what your body is telling you before it can no longer perform for you.
a) REST (I am aware that this is THE most popular choice)
b) train around it -- AKA become hench AF in one or both of the other lifts
c) sports massage
e) cool torturous things like acupuncture, cryotherapy, cupping, taping, Graston, ultrasound etc from the above folk
f) hydrotherapy -- get your ass in a pool
g) yoga/Pilates/Body Balance/meditation -- get your ass on a mat
h) do nothing and moan about it -- thereby rescinding your right to complain. It's like voting. If you don't make an effort, you can't bitch about the result.
Call these things ACTIVE RECOVERY. Sounds way cool, and you're thus more likely to do them. If you're not sure what might be best for you, do some research. Ask your chosen health care provider or therapist any questions you might have. Despite popular belief, we aren't all sadists, and we DO want you to get back to your training. We will ALL tell you to rest, so prepare yourself.
PS. always keep consent in mind, never endure a treatment or technique that is making you uncomfortable. You absolutely have the right to stop any treatment at any time, no matter what. You do you, fam.
If you're financially unable to pursue treatment, see if you can barter! Some therapists would be happy to do a direct swap for goods or services. Also, YouTube is full of good, basic and safe videos of stretching/Pilates/yoga, etc. Nae excuses.
"I had a session/treatment, but it didn't fix it."
Uh, wut?! First of all, unless you've gone to a surgeon, nobody can FIX you. Second, if all it took was one appointment to get people injury- and pain-free I'd have been able to cash out a decade ago! Accept that managing injuries and any subsequent secondary issues is a process. It will take time.
And the more YOU put into it, the faster it will happen. Do the stretches and exercises you've been given. Lay off the damaging movements. REST. Don't expect your therapist to be a miracle worker. If it took six months for the niggle to get bad enough to need work, it's not going to be undone overnight. Trusting someone else can be difficult, so (again) do your research.
"I damaged my rotator cuff muscle."
No you didn't. Depending on what you source, there's 4 main and 3 minor rotator cuff muscles. It's not one muscle. I promise.
"My glute/hamstring/lat/pelvic floor isn't firing."
You're upright, you walked in, therefore the muscles in question are firing. Muscles do not "turn off" (outwith of severe traumatic nerve damage or the like), but it is common for muscle groups to get lazy and have others be over-recruited.
Basically, be pro-active about your training. Try to recognise when it feels a bit wrong, and take measures to rehab properly. And for the love of the gods, STRETCH! Powerlifting as a rule seems to greatly reduce available range of motion, which can lead to an increased incidence of injury.