As someone who took clomid for several years, relatively unsupervised by 3 different doctors, let me say please please please, develop a relationship with a doc and maintain it throughout your clomid experience. I ended up with some serious reactions to the amounts of clomid I was taking, and I've lost an ovary because of it.
Any doc can prescribe. I think all of the doctors I saw were GPs. They should start you on a low dose and keep you on it for about 3 cycles, then up the dose if you aren't pregnant.
They doctor should ask you a lot of questions regarding how long you've been trying to get pregnant, and what you've been trying. Your age is important, too. When we finally did go to a fertility clinic, that doctor immediately suggested that we skip the clomid and try something more "aggressive" due to our age (over 30) and the number of year we'd been trying. "Aggressive" is not invetro. It was injectable drugs and an IUI. Voila- baby on the first round.
I didn't get a referral to the fertility clinic. I just went. And we paid for it, but it did almost immediately result in a baby. See if there's a clinic that will have a consultation with you before you commit to their services.