Carmarthenshire council voted in January to drop the English stream at Ysgol Llangennech, near Llanelli.
Labour said Michaela Beddows, who campaigned against changes at the school, is suspended while the party investigates.
But Ms Beddows has since told BBC Wales she is not a member of Labour.
Plaid Cymru's Jonathan Edwards wrote to Jeremy Corbyn claiming Labour members had been campaigning with UKIP.
He accused Labour members of sharing far-right material on social media, but said it was not "one individual" and called for more members to be investigated.
Ms Beddows spoke to BBC News about the council's decision on Ysgol Llangennech saying there was "no such thing as democracy in Carmarthenshire".
The Labour party said she had been suspended as a member, but did not reveal the reason behind the decision.
A Labour spokesman said: "The Labour Party is aware of complaints about Michaela Beddows.
"Ms Beddows has been administratively suspended from the Labour party while an investigation takes place."
Ms Beddows later said she was in fact not a member of the party, with Labour responding that, up until her suspension, she "had not notified the party that she no longer wished to be a member".
The Labour party has said a member has been suspended after a row over the decision to change a primary school to Welsh-medium education.