07 zx6r overheating

Hey guys, new to the forum and need some help. So I have a 07 zx6r and the other day I noticed my bike had gotten up to around 225 and pulled off to check it and there was some coolant on my fairing and even behind my fairing on the inside. So then I checked the reservoir and the coolant was way past the full line so I drained it to where it was supposed to be and it’s not leaking anymore but it is consistently staying at 223 degrees while riding. The fan is on and works but doesn’t get it back down to regular temperatures. The most i’ve seen it jump up to was 229 and it will not cool down until i’ve shut off the bike and for some reason my fan doesn’t run if I turn the bike off. Let me know if y’all have any suggestions.