I'd also add that when you feel a twinge/shooting pain, stop. That isn't the same as a cramp that you can just shrug off.
Just to prepare you, I doubt that your college doctor is going to be able to diagnose a specific problem. They will probably tell you rest and prescribe an anti-inflammatory and maybe a muscle relaxant initially.
You'll probably find that your local physical therapist will be able to tell you at least as much as they will be seeing more people with similar injuries. You'll almost certainly need to see a specialist if the problem persists to get a better sense of what is going on.
That said, there are a couple things to try. First, go see a physical therapist and get them to show you some exercises to correct any muscular imbalances, and work on strengthening all those little support muscles that help prevent lower back injuries.
You can probably do some of this on your own by looking for pre-hab, balancing, renegade training, but I'd recommend at least one session with at good PT to help you make sure that you're doing the stretches and exercises correctly, and tailor a program to your deficiencies and needs.
I have mixed feelings about chiropractors, but that is another option.
See if there is a good strength coach in your area, and see if they will observe your form and help correct any problems. While you may know what good form is, having someone watch you to see that you are doing it is another thing. Sometimes we do something we aren't even aware of.
I have a tendency to ever so slightly drop my left shoulder during recovery on back squats. As much as I concentrated on having good form, I was not aware I was doing this until it was pointed out to me. If you don't have anyone local, look for someone nationally to see if they will review a video of your lifts.
I'd definitely echo stuward's advice to drop the weight and concentrate on form. It may be that your form is fine, but some of the smaller support muscles are not up with your bigger muscles. This will give some time to let those catch up. Don't view it as a set back, as in the end you will end up further ahead than trying to bulldog your way through at higher weights.
Additionally, that strength coach will likely recommend some additional exercises to make sure everything is strong enough to support lifting heavier weights (these may overlap with what a PT advises, but there will be a few lifts I suspect they will encourage that the PT wont).
I'm almost certain that you'll hear Glute Ham Raises if you don't already do them. You may get told to do some variations on sidebends, iron crosses, seated or standing twists with bands or cables, etc. If you have a Reverse Hyper machine in your gym, take advantage of it. As most people don't, you'll have to settle for some of the pre-hab/re-hab exercises you find here and that a PT &/or strength coach would recommend.
Now the good news. Most of us have had at least one injury like yours. Those that are still doing this came away stronger and smarter than they were before. It is an opportunity to address any hidden weaknesses, learn how to deal with injuries better, and how to better prevent them in the future.
If your smart, this will turn out to be one of those important learning opportunities that begins the process of turning you into a grizzled veterans we all hope to become once we realize we can't stay young forever (I feel like I'm more grizzled than veteran, but I'm working on it despite a number of injuries and set backs over the years of training).