Tramadol is one of many medications to reduce inflammation and help with pain. To tell if it's working is a question for your vet. I would explain to your veterinarian exactly what you told me about her behavior (being comfortable in the morning and starting to limp more as the day progresses etc). He/she should be able to explain if that is what they wanted to see for her. If it's not, they will adjust her tramadol dose or try a different medication. Every dog is different. Some dogs' limps will do away and some won't. Your vet will probably know more than anyone else what you can expect.
This late in the summer I wouldn't worry about it unless her coat grows really fast, but it may be a consideration for next year to get her clipped by a groomer in the summer. If she's cooler, she might be more likely to sleep in her bed that way.
It's good that she wants to be active. You want that. But as you know, you don't want her to get too carried away. Does she eat whenever she wants? Right now I've got a young, very active dog that I'm trying to keep quiet while she heals from a cut on her leg. I reduced her food a bit because she doesn't need the calories to run while I'm trying to keep her from running! If your dog is eating a lot of high calorie puppy food, she's going to want to run it off.
As far as the doggie wheelchair goes, based off what you've told me, I don't think I would go that far yet. Wheelchairs are expensive, and at this point you've just learned of her condition and are just starting to manage it. If on down the road she gets worse, I'd look into again, but I'd hold off for now.