Well, I am not a big fan of trophies unless a person has actually won an event. I feel that it may lead a child to focus on external reinforcement rather than internal satisfaction with their efforts.
Getting a child into activities can be tricky. If she really does not want to participate and is miserable the whole time, then it is not a good fit for her. On the other hand, some children are just fine once their parents are not around
Is there something she likes to do on her own? Does she like to draw or color? Maybe there is a way to use the things she likes to do to bridge the gap to more interactions with others.
I'll give you an example. Two of the children at our end of the street decorated white paper bags (the size of lunch bags) and went around to some of us, offering them for sale for 25 cents each. One of the children was very shy and did not talk, and the other one was more outgoing. However, the shy one was very happy that we thought enough of their work to actually buy it.
The little boy next door is shy, but we've become great friends because I allowed him to set the pace. For example, I will sit on the driveway drawing with chalk. He comes over and we talk and draw together.
I would love to hear from some of the other parents, aunts and uncles, and so on.