If the software is running normal then the CPU may have gotten hot enough to be damaged. It depends on how quickly you shut down and how long the CPU was at 190+ if there is damage. I would suspect a DLL or other file to be using up CPU time and causing the lag. This could happen if you shut the computer down manually instead of the OS shutting it down.
You should replace the fan as it is not going to get better. You should also clean and reapply thermal grease to the heatsink and CPU. You did not specify an OS, but for Windows you can use Task Manager to see which routines are running, you can also use Resource Monitor to find out if there is an application or DLL that is causing the lag.