Yes.

From: Frédéric Buret: "Syphilis to-day and among the ancients, Vol 2-3 – Syphilis in the Middle Ages & Syphilis in Modern Times", Philadelphia: F. A. Davis, 1895, p.48:

The second proof emanates from a manuscript of which we have atready spoken in Chapter V of our first volume, and in which it is stated that the Dean of Windsor, Weston, was the most debauched canon of the time (1556), and much skilled in the art of treating Burning. He was himself the sultiect of it, for Cardinal Bernard Polus, who deposed him, says, in his order: "He not long ago brent a Beggar in St. Botolph's Parish." To express the fact that this same Weston had been heavily touched by venereal disease, the author employs a circumlocution which has long since become a proverb: "He had been sore Bitten by a Winchester Goose, and was not healed thereof." We are told by Beckett that at that time this was the "common Phrase for the Pox," because the stews were under the jurisdiction of the Bishop of Winchester. (emphasis added; "Pox" was one of the names given to the disease now called Syphilis)

And from: Matthew Lewis: "Medieval Britain in 100 Facts", Gloustershire: Amberley, 2015:

The prostitutes of Bankside became known as Winchester Geese and a dose of goosebumps became a euphemism for contracting venereal disease.

That means that the two stories are not so much in disagreement. The origin of this meaning we use today seems a little unclear – but widespread in many languages (Listed as in commonplace usage for German from the 16h century [Kluge/Seebald 2002]) This 'special' usage also fell out of fashion long ago (The practices of Winchester Geese outlawed in 1546).

"Was originally" might be a bit optimistic. Just change one word in the first article cited for the claim and you arrive at a factually correct statement for any case of the etymology: "the term 'goose bumps' was once (for a time) slang for the red bumps caused by venereal diseases."

As phrased in the question: the term “goosebumps” was used to refer to venereal sores.

Yes.

From: Frédéric Buret: "Syphilis to-day and among the ancients, Vol 2-3 – Syphilis in the Middle Ages & Syphilis in Modern Times", Philadelphia: F. A. Davis, 1895, p.48:

The second proof emanates from a manuscript of which we have atready spoken in Chapter V of our first volume, and in which it is stated that the Dean of Windsor, Weston, was the most debauched canon of the time (1556), and much skilled in the art of treating Burning. He was himself the sultiect of it, for Cardinal Bernard Polus, who deposed him, says, in his order: "He not long ago brent a Beggar in St. Botolph's Parish." To express the fact that this same Weston had been heavily touched by venereal disease, the author employs a circumlocution which has long since become a proverb: "He had been sore Bitten by a Winchester Goose, and was not healed thereof." We are told by Beckett that at that time this was the "common Phrase for the Pox," because the stews were under the jurisdiction of the Bishop of Winchester. (emphasis added; "Pox" was one of the names given to the disease now called Syphilis)

And from: Matthew Lewis: "Medieval Britain in 100 Facts", Gloustershire: Amberley, 2015:

The prostitutes of Bankside became known as Winchester Geese and a dose of goosebumps became a euphemism for contracting venereal disease.

That means that the two stories are not so much in disagreement. The origin of this meaning we use today seems a little unclear – but widespread in many languages (Listed as in commonplace usage for German from the 16h century [Kluge/Seebald 2002]) This 'special' usage also fell out of fashion long ago (The practices of Winchester Geese were outlawed in 1546, 300 years before the recorded modern usage of goose bumps).

"Was originally" might be a bit optimistic. Just change one word in the first article cited for the claim and you arrive at a factually correct statement for any case of the etymology: "the term 'goose bumps' was once (for a time) slang for the red bumps caused by venereal diseases."

As phrased in the question: the term “goosebumps” was used to refer to venereal sores.