Can I make see shirt sleeves tighter without making the body of the shirt smaller?

You can start by taking in the seam from the bottom of the sleeve working up the sleeve. If it needs too much under the arm you will have to go down the side slightly tapering it. Hope that made sense.

I have a long-sleeve tee like that. It fits well on the body, but sleeves are too long, cover my hands. I try rolling them up or pushing them up, but they always fall down. My solution is to put a rubber band around each sleeve before rolling it back. Helps it stay in place on my arm.

I’m no tailor but maybe cut the sleeve slimmer and leave the top, near the arm hole, wide? Like you’re extending the arm hole? That way it doesn’t effect the body.

cootton cna be either,, stretchy? probably a knit
not stretchy? probably a woven,

can you post a pic of it. Laid flat?

It depends on if there are side seems or if it is a rap around.

Knit fabric or woven?

Bring in the sleeve hem