I once fainted when a GP was drying one of my ears after syringeing them. That was over 40 years ago. She thought she'd gone too near to my ear-drum.
Nowadays, once in a while, I use bicarbonate of soda drops whenever my ears feel a bit clogged and that does the trick of softening it enough for 'home syringeing' using one of those Calpol syringes a coupe of times.
I probably shouldn't be encouraging people to do this but I've done it for many years now without ever having a problem. So long as the water you use and the syringe are clean....
Hope your dizziness goes soon.