if you have gum and someone asks for a piece, is it socially acceptable to say no? or is it considered rude?

i have anxiety and chewing gum helps me when i get anxious, so i always keep a pack on me. there have been times when i’m running low and really need it but other people have asked for a piece. i then receive dirty looks if i say no, but i don’t exactly want to share that i have a mental illness to a complete stranger. so in my opinion, it’s not necessarily rude. i think people can just be sensitive to being declined.