Its a Good Idea, first you need to check which tests needs to be done.
As
@Sunny6a mentioned, First you need to check with Panel Physician regarding which tests needs to be done and act accordingly. There are some tests like if the initial Chest X-Ray shows any scar then CIC prescribes tests for ruling out any active TB, the result for TB tests comes back in 65 days, follow up Xray is done 90 days after the initial Xray to compare that there is no change in the X-Ray. So I think Family doctor will not be helpful in those cases because you are going to loose time . As per my understanding visa doesn't gets rejected if a person is having active TB , person needs to undergo TB treatment for 6 months , re-tests are done and then visa can be issued once the cause has been cured because its a contagious disease and threat to public health .
If the follow up tests are for High BP / Diabetic or Heart condition then it makes sense to contact Family doctor.... I think in case of High BP/ Diabetic conditions they wanna make sure that it has not impacted Kidneys or any other organs, so Kidney related blood tests like Serum Creatinine or Protein via Urine test can provide your doctor with information about how well kidneys are working. Likewise there could be some tests for Heart condition.
These are my assumptions regarding various tests, I think every case would be different but it gives you some idea.
So don't worry and contact the Clinic first and check which further tests are required.