Praise be to Allah.
You should rest and then complete your tawaaf. If a long time elapses, then you must start tawaaf again from the beginning. But if your dizziness goes away quickly and easily, then complete your tawaaf and that will be sufficient, praise be to Allah. End quote.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him)
Majmoo‘ Fataawa Ibn Baaz (17/435, 436)