Hi Lab! The fact that you have thrown your hat in the ring is great! Having to make a map against is a deadline is the best way to learn....anyway it's how I did. Doubtless you'll have plenty of advice along the way, but my question is:
Do you know what you want your map to look like (stylewise) when you've finished it? Or are you winging it? (which is what I usually do). What is interesting about the coastline is that it looks very square on the pixels...which suggests to me that you're using quite a low resolution to draw the map (or have imported a low res coastline). It definitely looks vector.
Having a look at the tools of your trade, try this: print out the map at a very low opacity and go over the coastline with a black pen making it more curvy and wiggly. Scan it, and then import into Gimp (say 2000 by 2000 pixels in size). Use level adjustments to make just the coastline visible and then go for your fills.
It's a great start but I fear those blocky coastlines will come back and haunt you if you don't get rid of them now.