Idles higher than it used to?

My car starts fine after it has been sitting for a long time even in cold weather, but idles a little higher than it used to. When I start it and drive a short distance then turn it off, its difficult to get it to start and idle again. I have to hold my foot on the gas to keep it running. Eventually it will idle but fluctuates between 1100 and 1300 RPMs. It used to idle around 900. I also have an issue with the cooling fan not turning on (fan motor ok, relay ok). I don't know if the two problems are related or not. SOMEONE HELP PLEASE !