You can always try the covert route.
Be invisible by being visible.
That is, walk into the underwear section with a cell phone glued to your ear. Then say in a clear voice: "Hon, what size bra do you want? Oh, Ok. Panties too, got it."
Really, Really, REALLY, nobody cares!
When I go shopping for undies I sometimes find some guy GLUED to his GF/SO as she picks out stuff and he is trying so hard not to look at what he's looking at.
And at the checkout? When they ask "Did you find everything you were looking for?" Just say "Yes, thank you!".
It's really no big deal.
But in any case, congratulations on your first successful shopping trip. They get easier as you go on.
-Sandy