How to overcome fear of answering/asking questions in big class
There are several difficulties you're dealing with:


It is genuinely not easy to formulate and ask a good question. You know how they say that a good question is more than a half of the answer. That's why it is so important to learn how to ask a question and how to split a question in several smaller questions.
You usually do not have a lot of time in class as the lecturer tends to move on quickly. It is harder to come up with a good question in limited time.
Other students are also present and you may feel that they are "smarter" and they are "judging" you. Whether this is true or not, is another question (spoiler: it's probably not true), but the perception makes it harder to act.


Now, what can we do about it? My suggestion is to decouple the problems. First, start by learning to ask a question outside of the classroom setting. 


As soon as you have a question in a class, write it down on paper. After the class, re-read it, and try to find the answer yourself. Try also to re-formulate the question in a more clear, concise and answerable way.
If your professor offers office hours, attend them and ask your question in person. Talking to your professor one-to-one will help you both to learn the subject and to learn how to communicate more efficiently. It will also improve your confidence and build a good relationship with your professor.
When you are ready, ask more questions in class. Write down professors' answers and (if you have time) note your own reaction. Hopefully you will find it easier to ask questions as you do it more often. If not, meet your professor and discuss your questions again.