I had Vertigo in the last weeks of Paclitaxel and until 2 months after. It was relatively mild. Usually occurred when I turned over in bed. It felt like my head was spinning after turning over.
I also had a drop in my BP, early on with the Paclitaxel and required reduction in my antihypertensive drug. Before this reduction, I was occasionally light-headed.
There is also there is a condition known as Postural Hypotension, that you may have.
With this your Blood Pressure falls too much when you change position from sitting to standing, then you feel dizzy or faint.