I am a parent who is going through this issue with my college student. Your anxiety was high enough to cause you to withdraw. This indicates you need treatment. Likely medicine or therapy or both. This is not a mind over matter issue.
A few things we have learned:
A withdrawal for mental health reason is treated very differently than a withdrawal for physical illness at some schools. Make VERY sure that you understand and follow the rules for withdrawing and what has to be done to return. It is likely that due to requirements, you will not be allowed to return next quarter. Most schools want to see that the anxiety issue was addressed and under control before readmitting a student.
If the doctors feels medicine is indicated, they are likely to prescribe a fast acting (short duration) medicine and a long term (slow acting maintenance medicine). The issue is that everyone reacts differently to these medicines. It is very much trial and error. You might need to try several short term medicines to find one that works. You might find the medicines increase your anxiety or have bad side effects and that a different medicine needs to be tried. For long term medicines, they are likely to start with a low dose to see how you react. In 4-6 weeks they will reevaluate to see if it helped at all. At that point, if it helped at all, the dose might be increased and reevaluate again in 4-6 weeks. At that point, they could adjust the dose again or decide to start all over with a new medicine. My point in that it is going to take months to get the right medicine and the rate dosage. Adjusting to medicines while a full time student at a top school might not be the best idea. There is no magic pill that works immediately. The short term helps but it is not a long term solution for someone that has constant anxiety.
Like medicine, therapy will be a long process. It will take time to find the right therapist. Hopefully, you will learn non-medical technics to deal with the anxiety. Again, this takes time to learn and practice.
The reality is that it is highly unlikely you will be able to return next quarter. I would resist the temptation to return early thinking that the short term medicine will get you through. That is a path that could easily end in disaster.
Personally, I would consider holding off on CC and focus on getting your health under control. There are plenty of free online courses to look at to learn programming while you recover. Maybe a therapist can help you with that decision. Just because you feel that the courses are easy doesn’t mean that your anxiety will be any less. It very well could the same.
Based on what you wrote, this is not a matter of trust or loss of faith by your parent. They are clearly looking for the best path to help you achieve your goals. They are getting you the appropriate help and evaluations need to plan your recovery. It is EXTREMELY frustrating (for both you and your parents) that it takes time. You need to have faith that in time you will find what works for you.
Remember this is a bump in the road, not the end of the journey. You might need a different road but that doesn’t mean you won’t reach your goals.
Try to accept that this was not a failure. You develop a illness that prevented you from being able to function. You took all the right steps and got help. In my book, you did not fail. You are sick and are taking steps to get healthy.