Don't panic, the day of pins and needles is not a day of prickling and tingling of the limbs. It is a memorial day for the performance of the historic musical "Pins and Needles" in 1937 on Broadway.
The play, which was a musical review of current events, was raised by the union of working women in international textiles and performed by women who worked in the textile industry.
The International Workers Union Workers Union (ILGWU) was one of the largest and oldest workers' organizations in the US It was established in New York in 1900 to address the problems and hardships of textile workers (in these years only women were active in the field) They were unbearably hard (about the sweat workshops you heard?).
The women who usually worked in textile factories throughout the day would practice after work and appear in the evening.
The music and songs for the play was written by Harold Rome, who also wrote the book of the play together with Arthur Arnett, Marc Blitzstein and more. Link to more information