hi holly, i'm exactly the same. i'm really scared of passing out. the whole vision fading, feeling cold, lightheaded thing really freaks me out and has done for 4 years. i've only actually passed out once from shock, and i've almost fainted 3 times.
getting over anxiety is a long and hard process. try and be a bit more positive - going in the store alone is a big achievement, I can't even do that at the moment. praise yourself for the things you can do such as going for drives, going for small walks.
your lucky to have a family who support you. keep going out every day until it feels easier. then go a bit further, then try and go on a train for example etc etc
it is a long process, just keep going and don't give up. it will be fine one day.
p.s check out this book, it's very helpful: http://www.amazon.com/The-Agoraphobia-Workbook-Comprehensive-Program/dp/1572243236