I'm 15 years old and during the summer I've been working out with some dumbbells, and I've only been working out my arms for right now. Lately I have been feeling pain in my lower back and neck (which I do have a reversed curvature), but I would like to know if this pain is a side effects from just working my arms. Do I need to start working out other body parts?
When a person works on one group of muscles more than another, this person develops what's known as muscle imbalance. The human body has many muscles working together in order to carry out daily physical activities. For instance walking up a flight of stairs is more than just your legs doing the work, but also your core gets engaged to to keep you balanced. By you only working on your arms you are neglecting the other muscles that would usually work together with your arms, and as a result causing a muscle imbalance. What ends up happening is that the muscles that you are working out start to pick up the slack for the muscles that are being neglected and as a result they start to work too hard, and this eventually leads to injury.
Now I can't say for sure if your neck and lower back pain is a result of this (I have a strong feeling that it is, but I am not totally sure), but what I can say for sure is that you absolutely should start working on more muscles so that you prevent future injuries that can be a result of muscle imbalance.
It's not terribly convenient doing squats with dumbbells, deadlifts I find are a bit better (but I've also got long arms, so I'm well suited to them). If you're going to focus only on your upper body, given your age I'd suggest calisthenics - since you're still growing you have progressive overload with your bodyweight built in.
Also, it's quite impossible to really diagnose a problem like that over the internet (to say nothing of the fact that most of us aren't physicians), but for general purposes it would be more useful to know exactly what workout routines you're doing. Some upper body workouts could actually be quite balanced given that they're only focusing on the upper body, while others could be terribly imbalanced and could likely cause you pain even if you didn't have any pre-existing condition.