Not sure what is happening with temperature

I have a 2003 chevy cavalier. The temperature gauge in the inside of car always runs 195 but when at a red light it goes up to about 200 which is normal. Well yesterday I was driving it is getting hotter going up to 210 and not going down like it is suppose to when I start to drive. I do not feel coolant inside the car. The ac is blowing cold and hot. I checked the overflow tank it is normal. But I did feel the hose that goes into the engine there is still coolant in it when the car is turned off. Is this normal or do I have a real problem.