First off - don’t add thickness to clothing - it does very ugly things when animated:)
How you add the edge will depend on what result you want - piping or to fake thickness.
If its piping you want, extract the line, add thickness with 4 sides. If you want to fake thickness, extract the edge, make a tiny square and do a line sweep.
After this, the process is the same. Be sure to delete the row of faces on the back of the new shape which would be closest to the main body of the material - this is very important. If you don’t do that, you’ll end up with the dreaded non-manifold edges!
Move the new shape ever so slightly away from the main body of the material, so that the two shapes are pretty much touching. Weld, then average weld.
How you go about the UV mapping will depend on the general shape of the product, your personal preferences in UV mapping, how you want it laid out and how you are going to apply the textures.
In general, in Hex, you will end up with the back edges of the seam, piping or whatever it is tucked in behind the front edges, giving an overlap. After verifying the UV mapping, you can select one edge loop at a time starting from the one tucked furthest behind the others and move it outwards, then the next and so on until there is no overlap. Make sure that all the Edges are on the grid - anything off the grid won’t get any texture.
For more specific advice, please attach a screencap of the mesh in wireframe mode - a lot easier to help if we can see what you see:)