Your submissions are automatically recorded in Blackboard’s system, so no additional notification for a first submission is necessary. Your professor sees first submissions on the grading overview page.
You can check the gradebook on Blackboard to see what you have turned in. You will also receive a notification from Blackboard that confirms each of your submissions.
Your professor has far more students than you have classes. You can check your own submissions using the Blackboard gradebook. If you do not see a submission in Blackboard, you have yet to turn in that piece of course work.
Please watch the video to the right of this answer, which explains how to resubmit work on Blackboard.