an old shed has wiring
You haven't said how long the cable is, so you might want to punch your numbers into a voltage drop calculator and see what you get for voltage drop. 

Your power tools that have a 15A plug are likely only 12A, so use those numbers.  Most likely you are fine.

You are using "Romex" informally to describe all jacketed multiconductor cable. There are a variety of types and some of them are correct for wet locations, and others are not.  You need to be using a "wet location rated" type for the section that is outdoors.  

It is a fact of life that any conduit installed outdoors will most likely be full of water at least some of the time. That is why to use wet-location cable, it is made for that.