Hi @WendyBegy ...
If your instructor has set up the assignments in your course correctly, you shouldn't need to add them to your calendar manually. For example, in my own sandbox course (with an admin/instructor role), I created a brand new assignment called "Holiday Assignment". I set availability dates/times along with a due date. Then, I logged in as my dummy student account and navigated to the Calendar. This is what I saw:
The due date for the assignment is December 25, 2022 at 5:30 p.m. You'll also notice that it is green in color. This corresponds to the green course name at the top right corner of my screenshot...which is "Chris Hofer's Pandora (Sand) Box". The one just above it, "Chris Hofer (Dummy Student)" is the dummy student account. If I click on either of these colored boxes, it will show or hide those items on the calendar that are the same color. So, if I click on the green box next to the course name, it will hide the entry listed on December 25th. If I had created any personal calendar entries, those would have shown up in blue...and I can choose to hide or show those as well.
If you aren't seeing any assignments listed for your course(s) on the Calendar, then I would recommend that you reach out to your instructor to see if he/she has set things up correctly in your course.
I hope this will help a bit. Take care!