Is my Honeywell thermostat broken.?

I have a honeywell programmable thermostat and it summer time in Florida really hot. And for some reason when ever I adjust the temp for example if the recent temp was 78 and I set it to 77 or lower and the thermostat is reading that the house is 78 degrees inside, whenever I lower the set temp the indoor temp jumps up 2 degrees. And let's say I raise it back up to 78 from 77 or lower the house temp will read back to 78 or 80. It's a problem becaue if I try To cool the house down better like match upstairs and downstairs I can't becaue the temp just goes up every temp I drop it. And the unit run and runs and doesn't shutoff until matches set temp. It's a central air unit btw. And the thermostat is prob more then 9 years old. is it time to change it ? I think so . But I want to hear someone else's advice. Thankyou !