Same thing happened to me when I was growing up and my mum died. If you do the weekly shop at the supermarket together then just throw them in the trolley; you don't have to annouce it. Your dad will know about all that business, you know!

You could do your shopping on line and have it delivered, sell the benefits to your dad as saving time and money as you are not impulse buying. Then you can add your supplies onto the order. If this is a problem have you got a good friend who's mum can help. I have a teenage daughter and love being of help to her friends who usually find it more comfortable to talk to another mum than their own. She usually confides in other married friends so it all helps. I think lots of people would love to help you and it would open the way for talking to them if and when you need a bit of extra support of advice.

Your dad definitely understands that these supplies are a neccesity. Make the effort to join him on shopping trips, that way you can excuse yourself to go pick up what you need and simply put them in the cart. If you go shopping with him regularily, it'll avoid him having to pick them up himself(which ensures he won't pick up the wrong thing), and will make you more comfortable with making the purchase. If you're unable to go on the shopping trip, ask him if he can give you the money to pick up feminine products. Another possibility, if you're uncomfortable with making the purchase with your father is to ask a friend or a friend's mother to pick them up for you. Most women would be very understanding of your discomfort with the situation.

When I was younger and I lived with my Dad I would just put them in the cart while we were grocery shopping. He won't think it's disgusting or anything. If anything he'll be glad that you feel comfortable around him.