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I think I have the exact same combi drill and bits. The bits, new, made all the difference in my old flat where the shitty ones I had wouldn't even get me in far enough to hang a picture. But I wouldn't imagine they'd be any good on stone. As everyone has said, an SDS is what you want. they usually come with a couple of bits and a few chisel bits. I got the 5kg Titan one for about £60. That has paid for itself in drilling into ancient concrete and using the chisel bit to take down the old monster fireplace.
Shit drill bit? Doesn't even look like it's gone through the plaster. Get nice new masonry bits. Unless your wall is made of unobtainium (unlikely) or concrete (doubly unlikely in your place I would have thought) a cordless should be able to get through it.
Also try a smaller, sharper masonry bit first.