No you should not.
If you have received negligent dental treatment from your dentist that has caused you pain and suffering which could have been avoided, it is only right that you should recover compensation.
It is highly unlikely that your dentist will take it personally and there is no reason why you should not continue to remain with the same dentist if that is what you wish to do.
Alternatively, it is usually straightforward to transfer to another dentist within the same surgery or move to a different surgery altogether.
