In the day time you should wear a moisturiser with an SPF but make sure it is suitable for skin that is prone to break outs. You wouldn't want to wear anything that is too rich or creamy or heavy eg. products containing shea butter and cocoa butter. There are lots of moisturisers around with petrolatum in which is very comedogenic (ie will block pores) so get into the habit of scanning labels before you buy. Ideally you want something specifically formulated to help keep clear blemish prone skin. At night time if your skin is not dry there should be no problem leaving your skin without moisturiser. Alternatively look for a gel based product containing some anti inflammatory and anti bacterial ingredients to help calm and clear existing blemishes. Wearing make up is not going to help with the break outs but if you really don't like going out without anything on your skin go for mineral make up as this is non pore clogging.