Racing heart and syncope sounds like POTS - postural orthostatic tachycardia syndrome. Does her heart race when standing, but go back to normal lying down? Worth looking into. POTS isn't usually dangerous (it affects the heart's behavior, but is neurological, so her heart would be fine) but it can be very disabling. Sometimes it's easily treated.
Regarding the anxiety, I do understand your initial reaction. I would have said the same early on in my illness, but for what it's worth, I'll share how my thinking has evolved. (Your perspective might vary!)
Much like with pain, anxiety is absolutely horrible for the system, regardless of the cause. You probably are right that it's entirely Lyme-related and will resolve as the disease resolves, but it's a variable you can remove that will make those resolutions come faster. The physical and psychological are not separate spheres. Anxiety depletes the adrenal system, creates neural pathways that perpetuate symptoms, interferes with all types of hormone production, and interferes with digestions and gut health, affects the microbiome and immune system hugely, etc. If you can take the edge off with therapy, herbs, or meds to treat anxiety, then that should be considered as a way to ease the burden on your body.
This illness is a trauma. Many of us end up with PTSD from it. Anything we can to to treat that or prevent it is a good thing for our overall healing.
That said, finding a good therapist is another issue.... Some have good luck using the search filters on the Psychology Today search database, but word of mouth seems to be the best way to find a good one. Reject any stigma you may feel about
this. (I know how hard that is!) If you are considering meds, then I recommend a psychopharmacologist to prescribe, and a mental health counselor for therapy. A PCP or even an urgent care doc might be able to prescribe a low dose of a benzo until you find someone to consult with in more detail.
And also, you say you have so much to learn. We all do!
You are being such a rockstar parent, and I know that has to be enormously stressful for you. I hope you have support as you deal with all of this madness.