It sounds to me like you did pull a muscle. I pulled a muscle on the lower left side of my back on Jan. 3. I to was lifting more with my right side. I did it at work. I tried to work through the pain but with in 45 min. I could barely walk. Sitting or standing hurt to. I reported the incedent to one of my full timers and was sent directly to urgent care. I ended up having to file workmans comp, missed a week of work, had to go to the doctor 4 times and have physical therapy. Its a pain in the "you know what" but I am glad I did it.
If you have to lift for your job your back is the most valuable asset. The physical therapist told me that they know all the Trader Joes employies personally. Apparently at on point or another we all end up there. The same day I hurt my back one of my fellow employies hurt his shoulder and is still out.
The best advice I can give is, go tell your boss and have workers comp pay for it, since you did it at work. The last thing you want is for it to get worse from over use and not be able to work. It happens.
If you are worried about missed pay, don't be. I got paid half wages while I was out. Its part of the deal.
Accidents happenn, employers know that. That is why there are things like workmans comp in place.
I also found out that it is more likely to pull the muscle on the oppisite side from where you are lifting because it is straining harder. I don't understand how it fully works but it made sence when the doctor explained it to me.
I hope you get better. Just take it easy. Go to the doctor and find out for sure what happened. You will feel better.