'a bit of algae' will not do. Because what will you have left after he eats that? No algae, I can tell you that.
A 15G is also not big enough for them. And your water can not be fine yet. It takes up to 2 months to cycle a tank bettas, not 2 weeks. Plus they're sensitive fish, which means you want to put them in a lightly stocked tank, as opposite of your overstocked tank. They'll require a tank that has been set up for at least 6 months, in which you won't have a chance as high as you have that it will go into a mini-cycle again or that your water parameters change. He'll also Need de-chlorinator.
Untill you have de-chlorintor, a bigger and fully cycled tank, more filters and good knowledge about fish ... you should not be getting any more fish.
Sorry, but I've told you this many times already, on the forum, in PM and on msn ... if you're willing to mess around with the lives of fish that much, you're better off getting yourself a plant indeed. And even that will need looking after.