If you don't have enough storage to do an upgrade, then you have way more problems than too many pictures. Apple recommends that you keep at least 10% of your storage free, and I've seen my apps doing crazy stuff when I had only 150GB free on a 1 TB drive. This is something that you have to get control over, and you may need to get an external hard drive to hold your extra stuff.
You didn't tell us what sort of Mac you have. Portable Macs really need lots of storage internally, because you can't walk around with a hard drive dangling from a MacAir. On the other hand, if you're stuck, you have to do something. I have a 2TB MacBook, but I carry around a small, fast, light weight, low power 2 TB SSD like this:

This is from Amazon, and it was about $120. It weighs an ounce and it's about the size of a flash drive, 50x60mm. There are others, but I would get a well-known brand. I've been bitten by off-brands that cost a silly 10% less. If you have a desktop Mac, then you can use a larger, heavier, cheaper drive.
If you don't have enough room to put your stuff, you'll be spending way too much of your time shifting stuff around in a futile attempt to get more space. "Rearranging the furniture doesn't really make the room bigger."