If the size changes from say small to medium, does the shoulder to hem length change?
Title says it all. Appreciate the answers 
I'm a guy btw. I'm 15, 5'5 115 pounds, and an athletic build which in my opinion means I got lean muscle on me.
Generally, yes... but manufacturers can decide that lengths should remain the same in various sizes, or even get shorter as the sizes go up (which would be a truly odd decision, but it's possible.)
In general, yes, length increases with size, because the body typically gets thicker as sizes go up and you need a little more length to cover that increased thickness. To see this in action, stuff a folded towel under your shirt to simulate a heavier body build, and watch the hemline rise above the current location.
In general, length increases about 0.25 - 0.5" per size, depending on the manufacturer. "Better" manufacturers (the sort that sell to specialty stores like dedicated menswear shops) tend to cut longer than manufacturers selling to the
-mart shops frequented by bargain hunters. But this can and does vary widely -- each manufacturer is free to choose how they size and grade their patterns.
If you're the skinny body type (I was one of those), you're probably better off looking for shirts that fit you well and then noting who made 'em. With luck, all their shirts are cut similarly. Going up a size in order to get length is going to make you look like you're swimming in your clothes, which is probably not your best look.
At 5'5", you might want to look for clothing coming designed in countries with smaller people -- Italy, Japan, other Asian countries, etc. You're more likely to have luck there than with clothing designed in countries with a lot of tall, sturdy-built
people like the Dutch. I have a dear friend who can't buy clothes in the US easily -- he's of the slim and elegant build -- and instead buys most of his wardrobe each year when the family goes to Italy to visit a daughter. His wife, however, can't buy shoes in Italy at all... so they swing by the Netherlands on the way back home to buy her shoe supply.
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