There are two possibilities here, the first is BPPV and the second is a subdural hematoma.
Subdural hematoma is common in those after 70 after even a slight injury.
Since you had a fall and injured your head, and you are having symptoms till now, you definitely need a scan to rule this out.
I feel that your GP in fact should have ordered it then.
The fact that you had a second fall makes it even more important.
You should go to your GP at once and ask for a CT scan for this to be excluded.
The second possibility, which is more benign, is BPPV or benign positional paroxysmal vertigo.
This occurs commonly after a fall due to a dislocation of the balancing organ in the ear, the vestibule.
This can be controlled by medicines and adaptation exercises.
You now need to consult your GP and discuss about these two causes, subdural hematoma and BPPV. You should insist on a CT scan.
Meanwhile you should do some adaptation exercises for your dizziness, you can look up here:
Take care- be safe - note down these points and see your doctor and discuss with him/her - this will enable you to get an informed discussion leading to the best possible outcome.
Hope this shows you the way forward - wish you good health and a quick recovery.
I trust my answer has helped you gain more knowledge and confidence about your problem and in knowing what to discuss with your doctor.
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