Yea, you may switch. Myth is just a myth. With our first child, we did tell all of our family members, close relatives and friends since around 7-8 weeks. It’s up to you whom you want to choose to let them know. But, you should definitely let your yoga instructor know, cos some yoga poses are not suitable for first trimester.
You can switch as long as gynae accepts/have slots. Some gynaes don’t take in patients after certain weeks. I feel if it’s better to tell so she can look out for you during class. Safety > myth 😊.