@KS230 and @nelson28115 ...
There *might* be another way to get this information quicker, but it would still involve speaking with your school's local Canvas administrator. If your Canvas administrator uses this Guide:
How do I see which notifications have been sent to... - Instructure Community (canvaslms.com)
...then that person can type in your name in the "Search people" box and then click on the "Find" button. It would display any messages you have received from others via your Canvas Inbox ... for all courses you are enrolled in. For example, here is a recent message that someone sent me in my Canvas Inbox:

In the areas I've circled in green, you can see the message that the user sent to me, and you can also see the JPG file attachment that he included in the Canvas Inbox message.
There isn't a way to export all these messages to a file, but you could highlight and select (from the top of the screen down to the bottom) all the text instead of doing screenshots...and then go through them to filter out the ones you want to keep and which you want to discard. It might be a little quicker doing this than trying to grab multiple screenshots from inside your Canvas Inbox. So, I would suggest having a conversation with your school's local Canvas administrator at your school. Or, if you don't know who that is, try contacting someone from your school's Online Learning / eLearning / Distance Education department.
Hope this helps a bit. Sing out if you have any other questions...thanks!