I have lots of old flash and shockwave files I created in art school about 15 years ago. Now it seems like they are completely incompatible with any modern computer. Is there any way to vew these files or convert them to compatible file types?
"Is there any way to view these files?"
No. The browsers don't want you to use Flash Player for security reasons. After Dec 31st, Flash Player will be permanently discontinued.
"Is there any way to convert them to compatible file types? "
If you have the original source .fla file and you didn't use ActionScript to build complex interactivity, Adobe Animate CC allows you to publish Flash animations to both Flash Player and HTML5 Canvas. It might be a simple one-click conversion, but it's completely context dependent. You could download a trial and give it a shot.
Alternatively, if you don't have the source, they're just non-interactive animations, or something that would demo well as a video, you could just play them back and use a video capture tool to capture them as video content. The built-in Grab utility on MacOS would get it done. There are plenty of other options that range from free to paid out there.