With enough stress and anxiety and fear and worry your brain is basically retreating in on itself. Living with anxiety isn't living in the real world as it is. You live in a paranoid and fearful world that you're creating for yourself. By conjuring up all sorts of worst case situations and "what if's" and constantly focusing on the negative and downright scary.
Derealization/Disassociation/Dizziness etc. seems to be the mind's way of retreating from the excessive worries and stresses an anxious person puts the mind through on a daily basis. It's a sad state of affairs but it stands to reason this would happen. If you stress so much that you're causing physical pains in your body, why wouldn't your mind try and retreat from it all?
That giddy/drunken/lightheaded feeling is quite a common symptom with anxiety. But don't let it add to the worries. Just let it be, adding more stress will prolong it or make it feel worse. It'll kick in the fight or flight response if you fear it. When the mind and body senses danger you'll flood your system with adrenaline and various other chemicals we use to survive. Just let it be, don't let your brain fly at 100 mph with terrifying thoughts and fears.
yes it's not the nicest sensation, but it's not the worst either. Feeling a bit drunk for free? Enjoy it. That's right, enjoy yourself enjoy your life. let these symptoms come and go however many times in the day they feel like. If they stick around for days, weeks, months? So be it. i've had symptoms last over a year.
Acknowledge the symptom but don't rise to it. Gradually your body will realize it's not in danger. Don't feed the fears and worries and you won't feed your anxiety. Remember it's not in control of you, you're in control of it (the anxiety).