I think you might consider a smaller, less chaotic group until your child has the opportunity to accustom herself to other children.
- Invite one or two other children over to your home, and let her play
in that group. (Babies this age do not play with each other.) She
can become used to being in a small group in a familiar environment.
- Visit with the same sized group in other homes. Try not to hover. You do not want your daughter fearful or truly distressed, but you do not want to overprotect her either. As she becomes accustomed to these groups, add in another child or two to an already familiar environment.
- Find a quiet larger group -- like a reading to babies library group. Ask Library Staff if there is a play period before or after and don't attend that part until your daughter seems relaxed at the library and comfortable.
- Introduce your daughter to different environments in a safe way. Grocery stores, the park, museums, botanical garden or the zoo are all places that allow strollers (her safe place) but allow her to observe and involve herself as she wishes.
- Reintroduce Gymboree at a time of day that is less busy and work your way up to the same group.
I'd get started on this before you put her in daycare. I can't say what is exactly happening with your child, but many kids balk at changes to environment and noise or chaos. If you can be proactive without being too protective -- that balance will help you to help her gain confidence.
Shyness is a trait. There is nothing wrong with being shy. Dr Sears has an article here: Among other things he suggests:
To cure the shyness, you must build up the self-esteem. This child
needs parents he can trust, who discipline in a way that does not lead
to internalized anger and self-dislike.
Self-esteem is built up by encouragement and appreciation. Giving even a very young child choices (you pre-select -- there can be no 'mistake') and then letting her know she made a right choice. This also builds language. "You chose the bear." "You chose the red block. Good for you!"
My aunt 'taught' three of her four children to swim by throwing them into the deep end of the pool. The fourth never swam again and is still terrified of water fifty years later. Pushing children into things that they are not ready for doesn't make it work. Some do manage but sometimes it makes the situation worse -- it's a crap shoot. One size does not fit all and there's nothing wrong with taking a gentle approach while still helping her to do it on her own.