The light fixture popped and sparks flew, but the light was not turned. The breaker did not blow and the light is functional. Um, should I worry?

At first I was having trouble with my air conditioner blowing a fuse. (Yes, the previous owners left half of the house on a fuse box and put the half on a circuit box). I ran down to the basement and put in a new one and it would instantly blow agin. So… I unplugged the air conditioner cleaned the bugger out and then tried putting in a new fuse. Then I went back up stairs and plug the darn thing in and . . . poof! Sparks flew every where around the outlet. Now here’s the thing, I have been using that darn air conditioner all summer long with no problems what so ever. About 4 boxes of fuses (keep in mind there are 4 fuses per box) later. I now am unable to turn my ceiling lights on in half of my house. I would call an electrician but my stubborn husband won’t let me. He says it’s too expensive. Anyone have any idea what the problem is and how much it might cost me if I do call an electrician.