Shoulder dislocation injury

Hello! My story in short:  I was bouldering indoors, a relatively easy route that I could do with good technique on a sligthly positive wall. I had both feet firmly on holds and a locked hold for my right arm. I reach high above my head with my left arm, I touch it and *KLUNK* my left shoulder is dislocated. I'm confused for a few seconds, unable to move my arm and feeling really awkward. I jump down and as I hit the ground the arm falls and snaps back into place by itself. Some pain involved. I put pressure and ice on it immeadetly. After 20 mins I try to do easy arm rotations, no sharp pain but numbness and stiffness. Right after incident Next morning I find it painful and difficult to use my arm at all. Even raising my arm when lying on my back causes pain. After a few days After some Ibuprofein and a few days complete rest, the pain starts to ease. I can use my hand for light tasks. Putting on my shirt or jacket is difficult because of the complicated maneuvers needed to do it.  After 10 days (now) I can now use my arm for basic things without pain - cooking food, doing the dishes, washing myself in the shower, putting on my jacket and clothes etc. I still feel pain when I use force on some tasks, especially involving any outward-rotating moves, such as opening a sliding door. I also have to be very careful when washing my right armpit - reaching to the extreme right side causes pain and sometimes a slight feeling of *snap crack & popping* in the left arm. It's not really painful, although there is a sensation of "oops, better not do that". If I do movements with precision, slow speed and super-controlled, I can usually manage without pain. Any fast movements are likely to cause slight pain. I can do a full 360 circle with my left arm, though I feel that the angle is not as good as with the right arm, especially going upwards & backwards.  My question I believe it should be filmed with an MRI, to see what's broken, right? Since that is really expensive where I'm from, I'd like to know how dangerous in the long term is it to wait and see how it cures by itself, and start rehabilitation in a conservative way? Can I break something for good if it's not fixed in a surgery before doing rehab or light climbing? What are my odds of not needing a surgery? What would Dr. 8a do? I read somewhere that it's an indication of "no surgery needed" if the limb pops back to place by itself, is this true? Thank you for any answers and helps, over and out!