Hello max, I have a son who is 20 this year, and he used to face the same problem as you (small frame, skinny arms).

Then my husband bought him a pair of dumbells. He started doing 2 main exercises: 1 for arms, 1 for frame.

The arm exercise is just lifting the dumbell with the biceps. He does it around 10 times for 2-3 sets.
The frame exercise is lifting the dumbell with both arms from the side (like flying). Also around 10 times for 2 sets.
He does this every 2 days (exercise 1 day, rest 1 day).

Besides that, I have been cooking more for him and he eats 4-5 times a day. After a few weeks, he is much 'bigger' now.