Hi,
I suspect that you have been put on Dyazide to control hypertension (high blood pressure)?
Hopefully your renal function would have been assessed as normal before commencing you on these drugs, but if you have hypertension, then you should be having regular checks anyway.
There should be no problem taking these tablets and there should be no need for regular blood tests.
Of course, you just need to be sensible also and if you notice any unusual symptoms, then consult your primary care doc straight away.
Hope this helps.