You don't have to pick up the chips if you don't want to. While they are a nice reminder to ourselves of how far we've come and to others of how lasting sobriety is possible, at the end of the day they're just pieces of plastic and not worth causing this much anxiety.
One thing I love about the meetings in my current town is that they all say something that I'd never heard at other meetings before. When they offer the desire/24 hour chip, they always say, "I'm going to leave one here on the table in case anyone wants to pick it up after the meeting." It's a good acknowledgement of how stressful standing up in front of the group can be.
My personal advice is to just take a deep breath and get the chips at your next meeting. All you have to say is "Thank you for helping to keep me sober" and then sit back down and then all that anxiety will be over. You say you have a sponsor--I think it takes a WHOLE lot more courage to ask someone for help than it does to pick up a piece of plastic. You're doing great and keep it up no matter what decision you make in this case.