The best place to buy anything that you're too embarrassed to buy in person is the internet!
If you're worried people will give you weird looks in a store, find a website that sells panties and order directly. Nobody will know what's in the package — not even the mailman.
Benefits of Buying Online
- More variety in style
- More sizes
- You can probably buy panties made specifically for men
- Cheaper prices
- Nobody can judge you
- You don't have to hurry because you're feeling self-conscious
Alternatively...
If you don't want to shop online, you could always just go into a normal underwear store and act as if you're shopping for your girlfriend.
Nobody will know you're buying for yourself — just act confident, and stop worrying. People are usually too busy with their own purchases to worry about what other people are buying.
Staff in lingerie stores are used to men buying underwear for their girlfriends, and I'm sure they've also catered for men before, too.