A check-up most commonly refers to a routine general examination that isn't particularly focused in one area. That said, some sensitive/delicate parts of the body are routinely checked, so it would be possible to have a dental check-up, or an eye or ear check-up. It would be odd to have a check-up on a part of the body that does not usually see routine evaluation by a doctor, like the leg or elbow - if the doctor is examining your leg, it's usually because you're complaining about a specific problem, which does not fit well with the understanding that a check-up is usually a routine and exploratory procedure that's not intended to address a specific issue. A check-up implies that nothing specific is wrong, but checking one specific part of the body implies a specific issue.

If you hurt your leg and are seen by a doctor, it would be more common to say "the doctor examined my leg" than to say "the doctor gave my leg a check-up".

A check-up most commonly refers to a routine general examination that isn't particularly focused in one area. That said, some sensitive/delicate parts of the body are routinely checked, so it would be possible to have a dental check-up, or an eye or ear check-up. It would be odd to have a check-up on a part of the body that does not usually see routine evaluation by a doctor, like the leg or elbow - if the doctor is examining your leg, it's usually because you're complaining about a specific problem, which does not fit well with the connotation that a check-up is usually a routine and exploratory procedure that's not intended to address a specific issue. A check-up implies that nothing specific is wrong, but checking one specific part of the body implies a specific issue.

If you hurt your leg and are seen by a doctor, it would be more common to say "the doctor examined my leg" than to say "the doctor gave my leg a check-up".