I have to say, I'm definitely not an expert on Coin Magic - like you, I focus on Cards and a bit of Mentalism. That said, firstly, I'll talk to Amane when I get the chance and ask for his advice on what you should work on first.
In general though - and this can apply to any magic you perform - I'd take say the first two or three tricks you performed on the video, and look through them again, focus on them first. Let's say the first trick - Amane mentioned for example that when you slide the coin away, it looks a little funny. Try this: perform the trick for yourself, BUT where you would normally perform a sleight - don't. For example, where you would normally slide the coin - leave it there. Go through the entire routine like that - that should help you get an idea of what the routine should look like if it was completely natural. Then perform it again, and perform the sleights properly this time. Try to match the two, so that you performing the sleights looks as close as possible to what it would look like if you pulled no moves whatsoever - this should help with identifying moves that don't look "natural".
Something else you could try is this - say for example classic palm - holo I believe it was mentioned that it didn't look natural. Try walking around for a day with a coin in classic palm (I do this with cards sometimes). By the day's end, you should notice the coin less, and you should be dropping it less because it's spent so much time there that it should look more natural - being 13 it'll be harder for you since your hands will still grow, but that should help being natural again.
They're just some general ideas to try with all your routines - going through them and finding out what looks unnatural, and making them more natural, since you're not flashing anything - which is great - it's just that some stuff looks a bit unnatural - and that's a start. Remember - magic is much more than secret moves