Unless you are trying to represent an incorporated entity (a corporation or limited liability company, for example), you have a right to represent yourself in a litigation.
But you also had the right to do your own dental work. And I would expect the experience would be the same. Your dentist is going to be represented by a lawyer provided from his malpractice insurance company. So if you represent yourself, it'll be you versus an insurance company and its lawyers. Not good odds.
There are certain actions in which a party can represent themselves without substantial risk... a small claims action is such a case. Medical malpractice cases are not such a situation.
Ohio has VERY specific requirements in order for a party to file a medical malpractice case, in particular, under the guise of "tort reform." Therefore, it's very easy for you to case you to lose your case under circumstances that would not allow you to refile.
As such, I'm hard pressed to think of a situation I recommend against pro se representation (self representation) more than in a medical malpractice case.
If you are not comfortable or satisfied with your lawyer, by all means, keep looking. But I'd highly recommend against thinking about representing yourself. Medical malpractice cases require more than you just simply filing a complaint within a year. You NEED a lawyer.