Don't use heavy weights, use light weight and add slowly.
Fast forward a decade, and my right shoulder still remembers these pains - I dunno if the weights caused it or some previous injury, but when I started training with my own weight, one sign that I was getting ahead of myself was that small pain. Now I can progress slower, but still I have to be very careful. Some of the exercises with heavy weights are just not natural for the body and simply exhaust/strain it more than it should. If you are experienced, you can work around these limitations, but I prefer body-weight exercises now.
You were increasing the weights at a rate that your body couldn't handle. It is very frequent with new trainees because the neurological adaptations that appear at the beginning of training are always impressive: you finally learn how to use those muscles you always had and make them work towards a simple common goal, lifting that barbell. The main problem is that the rest of your body sometimes cannot keep up with that speed, and that results in this sort of issue. Had you been to a professional strength coach, he or she would have forced you to lower your pace and think about long-term progress over short term gain, which would probably have been at your 16 year old self's annoyance (as it was to mine).