It affects people differently. My brother is allergic to it and only had a raised temperature with a minor rash. I am also allergic to penicillin and it made me swell so badly I ended up on crutches as I couldn't bend my knee! So even within the same immediate family it differs. If you're in any doubt I would suggest you stop taking it and see your doctor as soon as you can, there are loads of alternatives for whatever is ailing you, though they do have a tendancy to give you thrush, just so you're prepared just in case.
Could your dizzy spell be related to whatever you're on antibiotics for in the first place perhaps? Just take it easy and rest.