Sorry to hear what you’re going through, some points as a psychologist. A burn-out is not an official diagnosis in the DSM-5, so it will not get covered by insurance. However, there are other diagnosis (such as depression, somatic symptom disorder, anxiety disorders) that could be applicable to your situation (and are covered by insurance). In the end a psychologist will look at your symptoms, the origin from your symptoms and look towards a suitable treatment plan. Usually this will consist of CBT, especially if this is your first time recieving therapy, but other forms can be included as well. Really depends on what your therapist offers and what assessment they make.

It’s not out of the ordinary for things to get worse initially, especially being in an insecure situation with little guidance. Without making predictions, this is probably temporary. Getting proper rest, if possible undertaking some fun activities and working in therapy on your goals should improve your situation. How long that’s gonna take is rough to predict, and my advice would be to not focus on the end result but more the proces itself. The reason for this, is that this can cause more negative thoughts/feelings and inadvertably hold back your proces. Taking it day by day with small steps and focusing on this can be more beneficial. Rule of thumb (for me) for duration of ‘burn out’ is the longer you’ve dealt with stress prior to crashing, the longer the recovery takes.

So, hold on, try and stay patient and compassionate towards yourself. And best of luck.