Possible blown headgasket?

Rebuilt engine with only 32000 miles.

radiator blew, engine overheated

replaced radiator, thermostat, hoses ok, but still losing coolant.
not dripping on driveway, overflow bottle empty one time and then full another time.
still over heats, but I always add coolant before I go anywhere. Engine runs great.
needed to add a little oil, but no water in oil
not blowing white smoke
warped head?
where is the coolant going? Have added gallons and gallons of the stuff.
Am on disability. Please help