No, it's from when you started originally.
My O2 will tell you when you can upgrade
If you have already upgraded to sim only from a previous contract you can upgrade to a Refresh contract after the first month.
Good news – you can upgrade today
If you call o2 they will reset your upgrade date from when you started.
Numbers here Guide: Coronavirus Community Help and Support
Track usage, upgrade and get support with the My O2 appDownload My O2