Hello Kacey. I think this is a promising start. Here are my own thoughts on some of the questions you have asked:
Well the short answer is yes. To begin with, when you are new to a discipline (in this case fantasy map-making) much of what you will do will feel unfamiliar and awkward. This is natural. The more you practice the more your skill will increase and the more confident you will become in the discipline.
Not all artistic pieces will turn out to be masterpieces. Nor indeed should one expect them to be. In the beginning stages of learning a new craft one should be striving simply to become competent in the fundamentals of the discipline. For fantasy map making this will include, among other things, learning some of the basics about geography (such as how continents work, where mountains typically form, the rules surrounding how water flows etc), and learning some basic techniques of illustration (you can find discussions on both of these things here in the Tutorials section). One should not expect one's first attempt at a craft to be amazing. The main thing is that through the process of creating the map (and doing a bit of research) you will become more familiar with geography and map-making techniques.
So yes, you should definitely continue to work on this piece.
The coastline could be a tad thinner. Mountain look fine to me, but it's your call.
Are you working with a tablet or a mouse? If you are working with a tablet, your stylus should allow you to control the width of the lines you draw based upon the pressure you apply. So tapering rivers is just a matter of applying different pressure levels at the beginning and end of your rivers.
If you are working with a mouse a different solution would be to manually erase the ends of the rivers so that they form more of a narrow point (which is what I did in
this map years ago before I had a tablet and had to make do with a mouse).
You can also vary the with of the river at various places as well to allow for lakes.
As to the texture overlay, is that overlaying the border or is it comprising the parchment? I did notice that the parchment looks slightly blurry. There are loads of free parchment textures on the web that might work for this piece, or you could create your own (in fact, if you search the Tutorials thread you'll find a few tutorials here on how to make your own parchment textures).
Keep at it, you are off to a great start.
Cheers,
-Arsheesh