Two sugestions; First look in the yellow pages under carpet repair. If you can't find someone there try carpet cleaners and ask if the do repairs. If that doesn't work try carpet store. Most have installers who work for them and would like a extra side job like this. A simple repair like this should be available for $30-40.
Second: Do it your self.
One Way. Now if the tile you installed is 1/4" or thicker (like ceramic or stone tile). Then you can usually simply go to the home improvement store and buy tack strip. It basically comes in two types depending on your floor. One is for wood subflooring and the other is for concrete. They come in 4' strips. You cut it out to fit around the edge of the tile. Leave a gap of 1/4-1/3" between the strip and the edge of the tile. Attach the strip around the edge and then cut the carpet back to about 1/8" heavier then the edge of the tile. Then you will tuck the carpet down around the edge into the grove made by the space between the tile and the tackstrip. The use of a knee kicker to tighten the carpet where you will miscut the carpet back too far can be used to stretch the carpet over the strip. This is the way a good carpet installer would do it in many jobs.
Another way. If you don't mind metal go to the home iomprovement store and buy a piece of metal to cover the edge of the carpewt and the tile. CUt the carpet back using a utility knife and put the metal at the edge.
There are more ways to do this depending on the flooring involved. I hope this helps.