I believe have a torn rotator cuff or at least an injury to my shoulder. should i go to the doctor?

i believe have a torn rotator cuff or at least an injury to my shoulder. i think i got it while weight lifting one day my left shoulder was really sore so i stopped my workout and went home. the next day my deltoid really hurt and i could barley lift my arm but i just figured it was from the workout. but when the pain continued pass the 4th day i started icing it every night for about a week. it started to feel better so i started lifting again and realized that my shoulder was really weak and i couldnt put up the weight i normally do. after doing those shoulder workouts i have alot of pain in my left shoulder to the point where i had to hold my arm up to make it less painful. its been about 3 or 4 week since the injury, i dont have any pain in my left shoulder anymore when i dont use it but when i lift weights or sleep on that shoulder for a while my shoulder feels like it on fire. i later did some research and found that a rotator cuff injury fits most my symptoms. also my shoulder makes a popping noise every time i move it around which i dont know if its related to the injury. i currently have no pain in my shoulder but it can tell that its still very weak and when i use it a lot i get that burning feeling right where the rotator cuff is. i haven't lifted hard in a while because of the injury but about a couple of days ago i did a couple of shoulder exercises to test it and i didn't feel too much pain but i could feel that if i lifted anymore i would have the same burning feeling in my shoulder. i would prefer to stay away from the doctor and take care of it at home but if seeing the doctor is the best choice for my shoulder to get healed than i will not hesitate.so with that information do u think i should go and see a doctor or can i take care of this injury at home and it will heal with time? thank you for helping me, i know it was a lot to read and i appreciate any advice you have for me about my injury thanx..