If you feel really embarrassed to buy condoms, there are many online shops where you can buy them in confidence. These shops will package the condoms discreetly in a brown box so the postman won't know, and post them to your door. Therefore if you’re of the lazy type you don’t even need to leave your house, so you can save your energy for the bedroom (or where ever). The credit card bill statement shouldn’t say what the item was that you bought, so if you’re planning on using your parent’s card you should be fine.
However, make sure you know when your purchases of condoms are delivered so that you will be there to collect it when it arrives in the post. Otherwise if you have parents like me, they will open them for you and they will find out which is probably more embarrassing than just popping down to the local shop and buying them there in the first place.