No need to make yourself suffer with the bad taste of garlic on what is supposed to be your break from the bad taste of Praziquantel! Seriously though, I'd just lay off the garlic and let your body recover from all the drugs, as garlic is more for killing bugs (mainly bacteria) and acting as an anti-inflammatory than it is for helping you recover (garlic can also actually damage nerves in high doses). If you've been ill for 10 years then yet another bit of of garlic isn't going to do much to help kill a worm, especially when you've just taken the real deal to do so.
You can transfer back to the NHS immediately after your first private consultation as just doing that saves you many moths of waiting, though you can talk it through with the doctor and decide what is best for yourself. I think they have some sort of rule where you can transfer private -> NHS -> private -> NHS a maximum of twice under the same consultant from private to NHS (though I'm not sure).