Shehzaad Bhatti, aged 33, of Kestrel Court, Apley, sent messages telling the woman that he "could not resist her", calling her "gorgeous" between September 13 and October 30, 2022.
He pleaded guilty during his appearance at Telford Magistrates Court on Tuesday.
The magistrates were told that the woman, who he knew, had blocked him and reported him to Facebook after messages on September 14 and 21.
But he contacted her again on October 29 with another Facebook account when he said he would come to her work.
Prosecutor Hannah Baddeley told the magistrates that the woman worked in mental health support and he had met her through that.
"It was not overly alarming but was unwanted and he knew that they weren't welcome," said the prosecutor. "There was some distress but not much and it was limited."
He had similar cases of harassment on his record, which she said were relevant for the magistrates to consider.
Jamie Wade, mitigating, said Bhatti has schizophrenia which affects the way he behaves and he is receiving treatment for it.
"He was interested to know why they had broken ways but he had not contacted her since being told to stop by the police," he said.
He said his client was on benefits and advised magistrates that a conditional discharge was in order.
David Silcock, who was chairing the three magistrates, handed Bhatti a conditional discharge for 12 months.
Mr Silcock said Bhatti was "not being punished for this offence" but warned him it could be considered if he was to appear before the court again.
Bhatti was ordered to pay £135 in costs and £26 for a victims' surcharge.
He was also handed a restraining order that prevents him from making any kind of contact with the victim for two years.