Mum I'm a long time sufferer of anxiety and IBS!!!
I, like you have the light head and fear of fainting. Can't tell you how many times I've literally ran out of shops, restaurants etc once the feeling takes hold. Many occasion I've filled a basket of shopping only to get a feeling of sheer dread at the thought of having to queue at a checkout and dumped it and fled. Once I'm outside I'm calmer but that thought trail is in my mind ready for the next time 
I take citalopram and have done for about the past 3 years. It does the job ok but doesn't completely eradicate the feelings of fear.
My IBS can be awful and my gurgling stomache is something else! I find that if I get a rumbling I have to eat as being 'hungry' makes me panic that I'm going to faint. I don't think that I'm really actually hungry as I tend to graze during the day but as soon as a gurgle starts I have to eat something. I've tried so many diets but so far it's still the same (going once a week, sorry for TMI).
Some days I'll be driving to work and know that I can't possibly sit in the office all day and find myself driving back home. I feel like a complete twat but once the feeling is there, no matter how hard I try, it's there to stay.
Trying to describe this feeling is so so hard and most people I know that I've spoken to think I'm some sort of weirdo (in my eyes anyway).
I would encourage you to take the meds described by your gp. You are not a failure in anyway shape or form and if the drugs help then so be it.
What I can say is that you are normal and there is no shame in feeling the way you do. I used to think I was some sort of freak but having looked on MN and on the net, there are so many of us like this.
I would like to get to a point where I can comfortably sit in a restaurant, coffee shop, wait in a queue etc without feeling the need to leg it, but I've tried therapy and hypnosis and whilst the hypnotherapy helped, I am not cured. I'm not sure I'll ever be cured but to take my meds and feel somewhat normal is a great help!!