New Thermostat issues when cooling

A few months ago I installed a programmable thermostat in my home because i was having heating issues. I had someone come over and fix it and everything worked fine.

But now that its hot outside, I my cooling is messing up. This is whats happening:

The Thermostat will read 80-81 when its not really that temp inside. So i turn on the A/C, cold air blows out, its working just perfectly fine, but the temperature on the Thermostat will remain 80-81 regardless of how cold it gets in my house. This causes the A/C to continuously run non-stop unless I manually turn it off. Simply put, it gets cold in my house but the Thermostat isnt changing temp.

I read about someone on here having a similar problem w/ an old Mercury one, but mines a brand new Honeywell digital one. Is my Thermostat faulty? The wires i connected to the new thermostat looked pretty old, but that seemed to be something I cant fix on my own, so I wanted some expert advice before I call out an electrician.

Thanks a bunch!