Can I install a 100 amp service in a laundry room that is 5 ft 6 in by 4ft

If the voltage is 240V or less, then yes you can. You need to maintain 36 inches of clear space directly in front of the panel with at least 30 inches clear width...
You can not install the panel directly above or below a domestic water line. Additionally, I would recommend keeping your distance from all water just for safety sake...