Q: AC/Heat not working anymore

I purchased my car used in February 2015. There were no reported issues on the car fax. In September 2016, there was a really bad smell coming out of the vents. It smelled like a dead animal. So we changed the filter that is under the glove compartment on the passenger side and the smell instantly went away. In October 2016 I got a service check and everything was fine. They replaced an air filter that was under the hood and that was it. About a week later my ac/heat will turn on whenever it wants. I would have to hit the dashboard, hit a really sharp turn or go over a bump/railroad track just to turn my heat on. (The weather is in the 30s). Now it will not turn on at all. Its hard to drive because it is freezing outside and I cant defrost my windshield without having the windows down. I have checked the fuses and everything seems fine. Coolant is good as well. I need a solution. What can I do to fix this problem in my car before it starts to snow?

My car has 113000 miles.
My car's transmission is unknown to me.