Use a good moisturizer, it shouldn't make you break out and it will help with dry/sore skin. I use Dr Hauschka, it's completely natural and it's brilliant, but it is expensive. I really think it's worth the money but obviously it's not an option for everyone. Clarins is also good, but expensive. You could try getting a facial aimed at helping acne. Again they can be expensive but you get really good skincare tips.
It's also worth looking at your diet. Intolerance to wheat and/or dairy can cause breakouts so you could try reducing the amounts of these that you eat. Drinking a lot of water is always good and should help the dryness of your skin.
I understand that it's horrible not wearing make-up when your skin is bad, but if you aren't going out try to leave your skin clear and make sure you remove make-up properly at night. Look at getting make up that is designed not to block skin/cause break outs. Bare Minerals is a good brand, clinique does good make up too. Also make sure you are keeping your make up brushes clean.
Ask your GP for a different type of antibiotic, there are lots and sometimes it's just a matter of finding the right one, i tried about 4 different ones over a few years. If you have been on antibiotics for a significant period of time and your skin is still bad, your GP may refer you to a dermatologist who can prescribe roaccutane (aka accutane). It's a stronger medication and can have quite serious side-effects but apparently it almost always works. Most people do one three-month course and that clears up their acne completely, but it causes dry skin and lips, it can cause hair loss, depression, thinning of the skin etc, so of course you should seriously think about whether you want to take it.
I hope that helps, I really understand how you feel and I know how horrible having bad skin is. If you have any other questions or anything i'm happy to try to help.