What have I been eating?

I have tried to find some information on the herb, garlic, but cannot find what I need.  I have this plant, and I have been using it as garlic. I can only hope it is edible, and I am sure it must be, since I am still alive, but I would love to know more about it. I don't remember when or where I first got the plant, but I have heard that chives have a round leaf blade and garlic has a flat leaf blade. I have found pictures of chives and they have a similar flower, only blue in color. So what have I got here? If it is garlic, I would love to grow more of it and learn more about it. I don't use a lot of herbs, but I do like to grow a few and use them occasionally.I have clipped the leaves of this plant and used it in various dishes thinking it was garlic, but now, I am not sure. Any help would be appreciated, but meanwhile, I will continue to do more research of my own.