I actually don't know, it's been my favorite/lucky number since I was a kid. I've really thought about it and tried to remember, I've asked my parents etc. but no one knows. It's a really cool number though, some random things:

The golden angle: https://en.wikipedia.org/wiki/Golden_angle

Age of the universe: https://en.wikipedia.org/wiki/Age_of_the_universe

The periodic table should end at 137 elements. Here's a good blog post about it: https://gravityandlevity.wordpress.com/2013/04/27/where-the-periodic-table-ends/

And here's just about the number itself: https://en.wikipedia.org/wiki/137_(number)

Here's a great video about 1/137: https://youtu.be/RCSSgxV9qNw

And an article (there are many more about it): https://science.howstuffworks.com/dictionary/physics-terms/why-is-137-most-magical-number.htm

There's a lot more where 137 pops up, but please don't take this as me thinking it's some deeper thing and that 137 is the truth of the universe or whatever else conspiracy mumbojumbo. I'm a science nerd and just think it's fun to have it pop up in so many places of importance, and I know most of those are via our own completely subjective measurement scales (a circle being 360°, measuring the age of the universe in earth years etc.) Some have asked if it has anything to do with 1337, and it has no connection to that.
I have a fantasy (as in it only exists in my head, so far) sci-fi universe that I've been developing for most of my life where 137 is important that I hope to do something with in the future. Like writing a book, making a game etc. all I can say is that blade runner and 2001 are major inspirations for it. I gotta head to bed but can post more fun things about it tomorrow.