Yes, Valacyclovir is an antiviral.
I share your doctor's opinion and I am also sceptical of homeopathy. The proposed mechanism is scientifically unconvincing and studies generally show homeopathy is not more effective than placebo.
I think CFS or possible chronic EBV reactivation is too serious to make such experiments, especially when there is a tested and tried approach (e.g., Valacyclovir).
But of course, the decision is your own to make.