My alimony and health insurance is going to be terminated at the end of this Dec per our divorce agreement. What happens if I can't find a job with health insurance... is there something I can apply for?

There are individual insurances and also state insurance if you qualify for that.

Also how it is being paid now, though his work or though a private policy he pays. Also you may be able to qualify for coverage under that current plan under what is called "COBRA" coverage but it will be costly.

There are 100's of private policies but depend on your age and health for the pricing.

It is paid through his work. We got divorced last yr and his work let me stay on another yr, but they said once Dec comes I have to go off it

That's generous for them to give you another year. Do you qualify for state assistance? Do you currently have a job? AFLAC has great insurance plans.