If little bit of filling over flows between the teeth, this will happen. It needs to be cleared from between the teeth and will be done by the dentist.
Next Steps
Go back to the dentist, and he may have to adjust the fillings between the teeth a bit. It can be done by the dentist only and you need not wait as it won't become better.
Health Tips
delaying will hamper, in between teeth cleaning and can cause decay over a period of time as you have rightly said