Hi there!
Personal opinion of course, but I'm all for going to the other doc too, so long as it's not a financial hurdle. Brace yourself for more annoyance, but...
You have a diagnosis which may help, if it gets you another prescription, that may help. If that particular doc isn't just a yes-man for the ped. you may get some more info at least.
I recommend taping your appt. so you don't miss anything important they may say. Including being dismissive. As for the endurance issues be quite firm that you feel a young healthy child does not become less fit for no reason.
Docs seem to lean towards a hypochondria dignosis for parents. If you can measure any change - like out running her brother vs. needing rests to walk, be prepared with that info.
If the tests they do seem senseless ask for a reason for the test. Point out that he does not know how strong your daughter was so all he can judge is how she is now. That does not cover change which is the problem which brought you here! Be a squeaky wheel.
Brace yourself for the 'antibodies mean she already fought off Lyme' argument too. It may be coming.
The notebook is a really good idea. Include temp. readings daily. Note what she ate if she gets stomach aches. Look out for moods and brain fog. Mention even fleeting pains. How many times did she need to sit on how long a walk?
I put all my notes on random paper and organizing it is taking time.
(I would love the template too please!) The idea of a graphic display of symptoms is outstanding.
A possibility for energy is a multivitamin in case she is depleted. Perhaps the ID will give her a broad panel blood test?
I posted a bit about manganese/magnesium in hemp seeds earlier. I don't know if it helps but the fact the Borrellia is Manganese dependent makes me wonder what it does to our supply.
Protein foods give sustained energy - more so than carbs which burn off fast.
Good luck. I hear from other parents that we can win this fight!