Try Kate Vincent at "Sew What!" on Back Street on the north side of the old football field. I know she does household sewing (cushions, upholstery, curtains, etc.), not sure about clothing alterations, but it's worth asking.
Elsa is the seamstress I have gone to for most of my alterations. Very inexpensive. She is just above Mickey's restaurant, speaks perfect English, just you must make sure she understands exactly what you want.
We have used Sew What but only for cushions and such. I needed some alterations on a pair a trousers and I needed it quick. I went to a shop almost across the street from the Belize Bank actually it is across the street from the Medical Lab just a little north of the Bank. They did fine and I was all set in a few hours. I think the name is Cloth to Clothes or something like that.