Right shoulder pain

4 months ago my right shoulder started giving me pain whenever I did pull ups.
Pain is there only when I do pull ups, or do the movement of pulling vertically with a small weight (30 kg at the lat machine).
It's not a huge pain but prevents me to do pull ups comfortably. It is located in the shoulder and in the armpit just above the tricep.
I stopped doing pull ups 4 months ago, rested completely for the last month. Pain is still there.
I do boxing 3-4 times a week for 1:30 hr, intensely. I use my right shoulder a lot, and I used to do pull ups once a week.
Have I damaged my cuff with over use?
Should I just keep training and not do pull ups?(that s what my coach said)
Should I not train at all for a while?
Should I wait if it gets better or seek medical attention?
I'm 25, always practiced sport 3-4 times a week,1 to 2 hours, rowing, gym, boxing.
Thank you for your help!

Ciao Alessandro,

Difficult to say over the internet. Minor lesions to the rotator cuff muscles are frequent even at your age. Often no symptoms are reported. You do a lot of physical activity and that may affect structures of your shoulder somehow.
I would advise you to have your shoulder checked to have a deeper understanding of what's going on with it.

Un saluto

Your problem may not be the triceps but either there teres group of muscles or infraspinatus insertion. It should be assessed properly since these are muscles that help to stabilize the shoulder so that it will move properly. You say your resting it but you are not. The thrust of boxing may doing as much harm as pull ups. Get it assessed by a physio not your coach.