What's the big deal, some guy notices you in the grocery isle and what? If you don't like being seen, then stay in your house. People can look at whatever they want to, and just because they take notice of you of the spaghetti sauce that you happen to be standing in front of doesn't mean they want anything from you.
Aside from all that, there's nothing wrong with talking to a girl that is with other people (family included). Talk is just talk. If someone makes an advance on you, you can reject them if you're not feeling it. I don't see what the problem is there... Thinking back I remember flirting with this girl across the dinning room of a sandwich shop years ago. She was out to lunch with her mom and dad. We caught eyes and threw smiles for a good 20 minutes while we were eating, and guess what when she went to leave, she let her parents walk out the door while she hung back and I got a chance to talk to her alone and get her number. Not all girls are paranoid like you.