My DD went through a shy stage from about that age as well. It seemed to go on forever, but in reality it was only a few months. We didn't really do much in the way of going out and seeing other people (still don't!), but in shops or the park people would say hello to her and she'd either scream the place down or try to hide her face in her buggy/my leg. It could be very embarrassing so I know the feeling there! Sometimes she would press herself right between my legs and people would say she was trying her best to get back inside me... She did it to DH too!
The worst bit - by far - for us was with my PILs. She adores my DM because she sees her all the time, and has never had a problem with her. In fact, she was one of three 'approved people' in DD's mind, the other two being me and DH. Her other grandparents, however, were another thing entirely.
She used to scream and scream when they came to visit, and it was so hard because I wanted them to see her and her to see them, but at the same time I wanted them to bugger off because she was getting so upset. Not their fault, of course, but it broke my heart. It used to take a good couple of hours for her to come around a little, and even then she wouldn't actually play with them, used to hide in our arms if they got too close, etc.
However, she's much better now, at 18m. She's started waving at cashiers, isn't terrified of her paternal grandparents, and I can take her out in public without fear of a huge meltdown. This all happened gradually, but as long as nobody touches her, she's fine. When PILs come over she's a bit shy at first, but only for a couple of minutes, and with no crying!
We didn't really do much, just warned people that she was shy (understatement), and took her out of the situation if it got too much. Not always possible, obviously. With PIL visits I used to take DD down one end of the living room and look out the window with her, so she'd get used to their voices. Then I would get a bit closer and a bit closer until she was in the middle of the room, still on my lap. We told PIL not to pay too much attention to her, and just act normal. Not ignore her as such, but chat to DH and I as if there wasn't a baby trying to burrow her way inside her mother's armpit... It seemed to work, but had to be repeated every time they came over.
I hope your DD becomes more comfortable with other people soon, it can be hard work, and absolutely mortifying when someone's trying to be nice and she's going barmy! 