Is it really possible you can have back pains unrelated to muscle tears even if you get them during excercise?

Yes: Actual tears in muscles are not common. Back pain that occurs during exercise is usually from muscle strain or sprain. Pain resulting from exercise is usually an indication that you are doing too much or exercises incorrectly. Pain in your back resulting from exercise should resolve with decreasing or eliminating the exercise which caused it. Moist heat and gentle stretching can be helpful.