What type of shirt fabric, size, etc to choose? ?

I have skinny arms and I want my sleeves from my t-shirt to cover the full upper arm. I own some medium and large sized t shirts. The large shirts cover all of my upper arm but are very big and baggy. On the other hand, my medium shirts look great on me except for the fact that the sleeves show half of my upper arm. It looks weird and I don't know which size to choose because there is no in between size. Maybe a slim fit shirt from hot topic?? Idk!!