I’ve been lifting for a while so have obviously done leg day before but I must have done something wrong last time because my lower back ****ing hurts. It was getting a little better but I did a full upper body day then ran 5k yesterday and now it’s back with a vengeance. Should I just do upper body workouts and just avoid exercise with my legs/back, just do light exercises like walking, or power through and go as hard as before?
Stop squatting (for now), and also don't try to substitute something like leg presses for squats as they will jam your lower lumbar spine up against an immoveable seatback and make it worse. Also, the 5k likely made it worse. Having trained over thirty years and trained athletes over 20 years, I've got a laundry list of injuries to myself and seen other athletes endure the same. These are battle scars. Each one was your fault and not the lifts performed and they are all meant to teach you something.
I'll say this with some reservation. See a doctor and if you can, one with a sports performance emphasis. If you see a doctor, still do so with some skepticism, and if surgery is suggested after MRI etc., seek a second opinion. I prefer a chiropractor instead and see one on a regular basis. As your spine gets out of alignment, you don't always realize because you are asymptomatic at till you're not. Often an acute injury was not really an "all of a sudden" injury. It was a progression from asymptomatic to symptomatic brought on by a activity such as a bad rep during squat.
If you opt to not take the above advice do the following. No excessive sitting or sitting period if able. Stand, walk, or lie down. When lying down on your back put a pillow or 2 under your knees. Walk 10 minutes twice a day. This will help realign spine and help circulation in the spine. *Don't stretch. Ice (Ice pack, frozen peas, etc.) for 10 minutes, then heat for 10 minutes at least twice a day. The spine gets very little blood circulation. The ice will reduce swelling and remove waste through blood by pulling it away and the heat will draw fresh blood back into spinal area. Be careful ingesting anti inflammatory OTC drugs. Use them sparingly for pain management only. You need some inflammation to heal.
While resting your back watch videos from Squat University or Starting Strength and start researching for the deficiencies in your squat. The reason I tell you not to stretch is because I'm assuming you don't know the mechanism of the injury. Back injuries from squat are caused by either flexion, extension, rotation with extension, or load (compression). So if your injury occurred because of excessive flexion (butt wink), then doing stretches like lying on back and pulling knees to chest, will make matters worse even though they kind of feel good. The reason it feels good is because the muscles tightened up around the spinal injury (disc) in order to protect the spine and do it's best to keep it from going into excessive flexion again. By stretching the muscles it has a more difficult time doing this.
Lastly, as you begin to feel better and study squat technique, start implementing the McGill Big 3 into your everyday routine.