Yes, it sounds like you have a blown head gasket which fills the heater core with exhaust gases causing the heater to stop working.
Here is a guide to help you confirm the issue:
https://www.2carpros.com/articles/head-gasket-blown-test
Please let us know what you find. We are interested to see what it is.
Cheers, Ken
Jan 4, 2018 at 3:06 PM