I'm old, but I did have measles, mumps and chicken pox.

Schools administering shots is an interesting topic. I did this bit of research:
The practice of vaccinating students in association with schools began in the mid-19th century in the United States, primarily to combat smallpox outbreaks facilitated by growing public school attendance.The earliest documented school vaccination requirements date to the 1850s. Massachusetts enacted the first statewide law requiring smallpox vaccination for public school attendance around 1855 (some sources cite 1853), making it a condition of enrollment to prevent transmission in crowded classrooms.
Earlier local efforts existed, such as Boston requiring proof of smallpox vaccination for school entry as far back as 1827.

These mandates typically required proof of vaccination (often obtained outside school), rather than schools directly administering shots. However, public health officials sometimes used schools as sites for vaccination campaigns during outbreaks.School-based vaccination programs expanded significantly in the 20th century:Large-scale trials and administrations occurred, such as the 1954 polio vaccine field trials involving millions of schoolchildren.
Later efforts included rubella and measles vaccines in the 1960s.

By the early 1900s, nearly half of U.S. states had school vaccination laws, and all 50 states implemented them by 1980, covering multiple diseases.Globally, similar school-linked mandates appeared earlier in some places (e.g., compulsory infant vaccination in parts of Europe in the early 1800s), but organized school-specific programs followed comparable timelines.This history reflects public health efforts to achieve herd immunity in high-contact settings like schools, starting with smallpox as the only available vaccine at the time.
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Polio vaccine was given us the year I turned ten, but we had shots in school before that in California. I don't recall how far back.

I remember in elementary school standing in line to get vaccines. Sometimes it was a shot, sometimes it was an air gun that blasted it through the skin. It was a pretty routine thing. This would have been in the early 70's

Wow, I never had a shot delivered by an air gun, that thought actually made me shudder. I remember during the draft, a lot of military draftees stood in lines and had vaccines injected via the air gun........they didn't like it very much.

Before we went overseas, we stood in line for the gun injection. It was a bit painful, but I would have selected it over individual shots, of one for each of everything.

I was definitely one of those who didn't really like it. Sometimes those air guns would leave a visible hole in your arm.

I was enlisted in AF on Xmas of 1970. They sprayed the shots and warned you not to flinch or move. Yeah, right!