You wouldn't need a general checkup before seeing a sports doc, and I'd personally skip straight to a sports doc... since you're talking in terms of exercise specifically, not just general pain, I would seek out their advice. There are certainly general practitioners who would be skilled enough, but doctors with a specialty in sports medicine will just be getting straight to the point. My GP is a runner, so I went to see him the last time I had a running related injury because I knew he would get me when I told him "it's four weeks to the half-marathon and it hurts," but if I hadn't known he was a runner I would have gone to a sports medicine clinic here.
If you don't need a referral from a doctor to a PT (some states/insurances require you go to a doc first) you definitely could go straight there. The only reason I suggested sports doc first is because a PT is (usually) not a PhD and technically can't diagnose most things. Also rarely do they have access to x-ray/MRI equipment should you need it, so they'd refer you back to a doc if they felt it was necessary. X-rays can also sometimes give extra information to a PT, but it's not required.
For my running injury, I went to my doc first because I thought for sure he was going to want to order an MRI. He didn't, but he did prescribe me a short round of steroids and recommend me a PT who was also a runner (we like to stick together, you see, LOL.) Honestly, you could probably go either way... the sports medicine clinic here is actually mostly staffed by PTs and OTs and they handle most of their clients.
I'm not personal trainer certified so I can't LOL.
I've thought about it before though. There's a program at the local community college and it's only a year. But I can't afford it and the only financial aid I qualify for is a loan... which I am not on board for debt. =P