I'd probably suggest speaking to both your GP and dentist, as depending on the cause it might be more appropriate for one or the other (but both may be able to suggest methods to manage the issue in the meantime). I'd suggest making appointments for both, although I imagine you'll probably be able to see the dentist sooner (GP surgeries always seem to have fewer appointments available at shorter notice). While you wait you may also want to try and see if getting a differently shaped brush, or changing your toothpaste brand/type/flavour helps.