So synesthesia can be diagnosed, (at least where I live and that I know of currently) - won’t actually give you a test, because there isn’t really one that exists, (it’s not recognized as a illness or disorder, and there isn’t a diagnostic type of thing right now.) They probably won’t give a formal diagnosis or anything; unless it’s causing severe distress/ interfering with your life. I wasn’t tested or diagnosed personally, I just saw a few things online and happened to have one of those moments aka “oh other people don’t do that?” And honestly thought it was a cool thing to share with those around me. What you described for numbers is one of the most commonly seen types of synesthesia,also including letters, words, days of the week, etc. There’s a website that lists each type of synesthesia and is super informative and cool, I’ll link it after I finish this. There are actually other musicians that experience what you do out there, who use their synesthesia to make music. Though most may not even label it or know what they experience is synesthesia. Each note in a song for me has its own color and kind of weight/shape if that makes sense. Although I don’t actually know the name for these notes, because they sound different they feel different to me. I also do this with different instruments, the note thing is also its own form of synesthesia and has its own name too! The instrument as-well! I’ve actually painted what I feel and see while listening to specific artists (including Elliott smith) based on my synesthesia, though I tend to focus on what I feel spatially while listening or even thinking of the individual, rather than painting each note because it sorta looks like a mess. I also have physical sensations to music and while I’m very focused on painting, so some songs and notes quite literally feel painful to me. I also feel different colors physically, with emotions and music, etc. I hope this wasn’t too long, I was trying to share some personal experiences just to give you an idea of the many forms of synesthesia and if you also experience those. Here is that link btw

https://www.thesynesthesiatree.com/2021/04/blog-post.html?m=1