If I do an exercise using only one side of my body, and i can do more repetions with one side (for example: I can do more reps with my right arm), should i only do as many repetitions as my weaker side masters, or should I continue to work with the stronger side, when the weaker side already can't go on?
Exaggerating imbalances is generally not something I want to do. If I can do more pistol squats with my left leg than my right, I'll do some extra pistol squats and lunges with my right leg to catch it back up to speed. The same goes for arm work like overhead presses. In practical terms, I accomplish this with extra sets on the weak side, rather than trying to eke out extra reps in the existing sets.
I would recommend to use a barbell to train your both arms at the same time orient around barbell oriented compound multi-arm movements like barbell curl, preacher curl, ez-barbell curl. If you don't have access to that, get a broomstick, fill 2 identical bottles with water and tie them on to the equal ends from each end. Do a lot of high repetitions (either 2+ sets 21(7-7-7) see this for further reference or 3+ sets of 15 reps each till you have the feeling that the strenght is well balanced)
But also please see a doctor to check whether your motoric and parasympathetic nervous system is in good order. It might also be caused by a disorder or a nerve issue in your neck.
@All comments below my answer: Appearently I had to re-vise this which might come due to my short-circuit explanation. After being an Olympic trainee for martial arts for more than 8 years in my youth, and seeing hunderds of Olympic sports doctors and physicians and therapeutics who taught me thoroughly on how to observe imbalances in my body and take action to recover, I just shared my conclusions. There is not a side less stronger than the other in human body, mechanically unless there are multiple imbalances or a disturbance in nervous system or blood circulation issues..... period! And if you have mobility issues due to other reasons that I stated below, than you should find the cause and take action.
Many of those imbalances come through irregularities in lifestyle (a Quagmire arm to Google for e.g.). Also many see symptoms for a cause which ends up in either having extra injuries on top or turning injury to inabilities. Preventing an injury does not only depend on the good form but also on the good choice of right exercise at the right time and knowing how the kinetic chain of a given exercise works to observe whether you are doing your reps in good form or not. Working out is not only fiddling around with weights, when done improperly, you end up wasting your time and money...
Why do I get the feeling that no one has taught you folks about the "human body adaption and recovery?"
And what's wrong with advising someone to see a doctor? are we here to give advise as professionals?
In case you need more thorough explanation or references in case you have the feeling that my explanation comes short, feel free to request and I'll make sure they will be added in my answer. For the sake of convinence, I'll just keep the post clear of confusing proofs...
P.S.: Also, it is good to have the "Atlas of Human Anatomy" by Frank Netter, MD (3rd edition) at home if you wanna understand your body more.