Is my car overheating or is it a false reading from temp gauge?

97 Accord 4cyl -I replaced the distributor because of an oil leak on my Accord- After removing dist, I noticed that both temp sensors that sit right underneath dist had been damaged by the leak. The coolant temp sensor was dangling and broke off. The other is temp gauge sending unit, different style and only connector was beat up. I cleaned it and seems OK. I did have to replace broken one. Since then, now temp gauge needle moves up or down according to speed I’m driving. Goes up to about 75% when driving on freeway to about normal 25% when driving in slower traffic. Needle moves fast one way or the other when changing speeds. Coolant is OK in radiator and reservoir. No leaks, oil or coolant. Upper radiator hose feels hot to indicate thermostat is functioning ok? Another problem I've had for a long time but gotten worse (even before sensor problem), fan stays on for 10-15 minutes after turning engine off. Could this be related? When I found and replaced the broken sensor I thought I had found that answer but little did I know that I would end up with more problems. Maybe this new problem was always there but because of broken sensor I never knew it? Any ideas would be appreciated. Thanks.