I use the prescription-free pharmacies listed in
this post to by my meds. But if you go down that route, the onus is then on you to make sure you know what you are doing (eg, checking for drug interactions, side effects, etc). Some of the antivirals require regular kidney or liver checks, so you need to bring your GP on-board anyway.
Other meds like oxymatrine (for coxsackievirus B or echovirus) are supplements that you can buy online.
The main viruses in ME/CFS are 3 herpesviruses (EBV, cytomegalovirus and HHV-6), which can be tested for in the UK, at places like The Doctor's Laboratory in London and Manchester; and enteroviruses (coxsackievirus B and echovirus) which can be tested for in IMD lab in Germany.