Personally, if I were in your condition, I would wait and keep detoxing and taking anything anti-inflammatory like fish oil, curcumin, quercetin, and antioxidants like Vit C.
Bar-1: I've never taken this. I know your doctor recommended it, but I would not recommend a formula for someone with severe herxing, especially a formula that is expected to be strong and causes herxing.
Only you can decide what to do. I would recommend getting Stephen Buhner's books on Lyme and coinfections, if you can afford them. They are reasonably priced. You need to have reference books like those, so you can learn more and be able to help yourself with or without a doctor. In my opinion, doctors tend to shy away from Buhner because they can't control him, and he puts the power in the hands of the patient. Doctors like patented formulations because they know exactly what and how much the patients will be taking, and therefore the doctor is in control. IMO, what is safe and convenient for the doctor may not be safe or productive for the patient. That's why self-education is so important with these infections. For most on this forum, treatment has not been short or easy. Many are like you and have complications that hinder treatment and make getting well more complicated.
Buhner outlines ways to reduce cytokines which cause inflammation and symptoms, ways to correct the abnormal immune responses that the various infections cause, ways to support your organs that are being damaged, and lastly ways to kill the infections and stop their activity.
If I were you, I would continue taking anything you already find helpful and the skullcap and lemon balm you mentioned. I assume it's Chinese skullcap. If it's American it won't work. If you're not taking milk thistle and hawthorn, start those to protect your liver and heart. If you haven't tried kudzu root, try it. It has helped my head symptoms. I'm using a tincture - 15-20 drops. Red root may possibly help your specific symptoms as well. Peteza said that helped her head pressure and pain. If you have problems with blood coagulation, skip the Red Root. Buhner says Japanese knotweed can specifically help brain and head inflammation, but some are sensitive to it, so start slowly.
You could get the following herbs from Buhner's trusted sources (Woodland Essence, 1st Chinese Herbs, Mountain Rose Herbs, etc):
Japanese knotweed (he prefers whole herb in powder form from 1st Chinese)
Danshen/Chinese skullcap combo - Woodland Essence has this
CSA Formula and Houttuynia OR IHA Formula and Sida Acuta (woodland Essence has these)
Either of those groups will treat both babesia and bartonella.
Start with small doses of Japanese knotweed and danshen/skullcap and increase slowly until you feel better or worse. Then slowly add TINY doses (start with one drop) of whichever formula you get and slowly increase. Next, add the companion herb with the formula you chose.