You don’t necessarily need a ring flash. I got by for ages without one. I assume if you are in a dentist surgery you’ve got plenty of light available.
It’s worth noting that bridge cameras are all capable of very good close-up macro work out of the box – capabilities that you would have to spend a lot of money on a second lens for a DSLR to get.
I bought a LED ring light from Amazon for £40 btw, as opposed to £200 for the Olympus ring flash unit. Works nicely and is on all the time so lets you set the shot up.