Honestly: I think every sort of die rolling that can be tried has been tried, so the concern is less 'is this new and interesting' and more 'does this make the game play the way I want it to', and we know nothing about the way your game is supposed to play outside of the die mechanic.
Nothing wrong with it, though I'll note that an advantage/disadvantage on a roll works out to a +2/-2 bonus on average.
That said I'm not fond of the idea of adding the skill to a 2d10 roll. Usually when I see 2d10s there is a roll over or roll under mechanic involved. Examples off the top of my head include Corporation, SLA Industries and the 3rd Edition of Mechwarrior (The fourth kept a similar mechanic with 2d6s, as I recall), along with a few more minor examples. I can't think of any which used 'add skill', which as you describe sounds more like a take on the D&D mechanic, only swapping the d20 for the 2d10.
Adding additional die as a levelling mechanic is doable but, in my opinion, unadvisable. I've never seen a popular system that used growing mixed die pools, but then I can't think of any that did it as an optional mechanic instead of core (see Alpha Omega, among others...). The closest currently 'successful' system I can think of that works like that is Modiphus's 2d20 mechanic, which only grows by adding additional d20s, rather than mixing dice.
Hope that was useful, and good luck with your design.