are you taking any antidepressants, together with alprozolam? This medication alone is a sedative, and depending on how much you're prescribed to take daily, it's quite possible that the medication is causing you to feel lightheaded. If you look at the patient leaflet, you'll notice that dizziness and drowsiness are at the top - and there is a warning not to operate any vheicles while on alprozolam, so - now you know why they put it there.
If you can talk to your doctor about lowering the dose 0.2 mg or giving you a prescription for another anti-anxiety medication, you might solve your problem, at least with the dizziness.
Hope things get better,