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There is no relation to the surgery or the medicine...
'Giddy' is vague term - unsteadiness. If there is definite sense of rotation, it is vertigo
. If it is from getting up from bed, it may be from postural hypo-tension.. Did you check your BP?
It can be from anaemia
– what is your haemoglobin? Has an ECG been done?
The body's balancing mechanism is in the inner ear
. An ENT (Ear Nose Throat) specialist is the one to see - especially in the presence of tinnitus
. They have special tests to confirm or exclude the contribution of the ear - which probably is the case with you.
If there are no clues, you have to be followed up by a neurologist
Wishing speedy recovery