Can I have emergency breast implants removed?

More information will be necessary to give you meaningful advice.  There are very few cases where emergency breast implant removal is indicated.   Best wishes.

Implants can be removed for variety of reasons. A true emergency includes hematoma, hemorrhage, infections, severe scar tissue leading to exposure or skin necrosis. Seek local plastic surgeon to determine your situation 

Situations already mentioned would be reasons to remove them emergently. Removal of breast implants is a fairly short procedure.  If you simply want them taken out quickly for personal reasons, you should be able to find a plastic surgeon that can help remove them soon.