First, buy yourself a decent drill. The drill set you used was probably cheap, but it's rubbish.
Best to get a four-edged concrete drill bit from Hilti or another high-quality manufacturer. It might cost 10-12 euros, but it lasts three times as long. Everything else is simply no fun and won't get you anywhere.
They all have SDS shanks, but if necessary you can also put it in a normal chuck of a hammer drill. Without a decent drill bit, the best drill is useless to you.
You only need a 6mm drill bit, maybe 8mm, for a lamp fixture.