Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
What shirt did you print on? It doesn't look like a 100% poly shirt from the picture I could be wrong.
Others will get on here that know more than I do to help out. But I don't think I see dye migration problem as much as a ruff print/ fibrillation problem. The more detail on how you are printing the better help you will get. mesh counts, inks, manual auto etc.