Unfortunately, an initial increase in anxiety is very common due to the enhanced serotonin activity produced by serotonergic antidepressants (ADs). Despite the common myth, serotonin isn't a 'feel good.' However, the body, including the brain, usually adapt to the increased serotonin by downregulating serotonin synthesis and expression after a while and the anxiety and other side-effects then diminish, but may return for a while after dose increases.
ADs typically take 4-12 weeks to kick-in and given you've been on escitalopram before (it is also the active ingredient in citalopram) kick-in may take a little longer than the first time.
ADs have no direct effect on anxiety, or depression in the way say aspirin has on a headache. They work by stimulating the growth of
new brain cells (neurogenesis) to replace cells killed, or prevented from growing by high brain stress hormone levels. The therapeutic response is produced by these new cells and the stronger interconnections they forge, not the meds directly, and they take time to bud, grow and mature. For a more detailed explanations see:
Depression and the Birth and Death of Brain Cells (
PDF) and
How antidepressant drugs act.
Dizziness is both an anxiety symptom and common initial antidepressant side-effect, probably mostly caused by the heightened anxiety than the med directly.
Imo, the best course is treating the side-effects rather than abandoning the AD and your GP should be able to help you with this.