Ha ha
Guess what? I was about to type the below when I suddenly realised I didn't know if you're a guy or gal. Went to your profile, not indicated.
Searched for all your posts and was kinda certain you're a guy from the Masturbation thread haha
So hopefully I'm right that you're a guy, right?
Hmm, self-conscious or not, maybe this suggestion can be useful for you:
Carry a bag (either a brief-case type or one with sling) so one hand is holding on to the carrier or the strap. That leaves the other hand which you can either put it in your pocket or just swing freely while walking.