I injured my back (l5-s1 bulging disc). I feel the pressure on my pelvis and lower back especially the left side w/o pain? Will it go away with time?

It's possible. It depends on the extent of your injury. I would ask your doctor. I assume that u saw one to make the diagnosis. In general, young adults should avoid surgery if possible. Physical therapy often does great things for back pain. Ask your dr about pt.