sorry then it's your heater core leaking.

you could clamp both heater hoses, so it won't leak while you finish driving the car this year.

I suspected my heater water valve was internally leaking, allowing some hot water to go through the heater core while I was running the AC. So clamped them off temporally. I used 2 old water bed wood frame brackets I had laying around. Looks like crap but works.
You could do something similar until you take out the heater box to replace the core. Good luck.