You can ask your doctor for anti-anxiety medications that can help such as Lexapro, Celexa and Pristiq and do not have the drowsiness effect .
Valium is also causing least drowsiness.
Even Buspar is less sedating effect than other medications. It also has low risk of dependence.
However you are not feeling well then you can discuss your symptoms with your doctor and if required your doctor may switch to other medications as well.
Regarding your dizziness,your blood pressure should be monitored and other possible causes may include Hypotension,Hypoglycemia,BPPV,Inner ear inflammation to rule out.
You can also go for pyschotherapy,meditation,yoga,deep breathing exercises which relieve anxiety.
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