If there is really an urgency, like you are losing time then this can be done, CHC would not have any problem with that. Also, in their medical letter CHC sends, they have mentioned if for some reason you are not in your city to get the medicals done, you can always go for another place. there is no restriction on that. Anyways if you have sufficient time and want to by consultant's advice, that is fine. I just suggested what i felt was right in case there is an urgency. You better follow consultant, so he does not have a chance to blame you in case something wrong happens.
Best of luck for your medicals.
Vishesh