Tell your manager.
Why to let your manager know
Overloaded does not need to mean that you are unwilling to complete the work or are incapable of managing it yourself, but it could indicate that you need some assistance with prioritizing.
Hiding your burden from your manager will not solve anything, as they will either:
- Notice the drop in quality/increase in your stress and jump to their own conclusions
- Not notice that you are overworked and send even more assignments your way
Raising it directly with your manager, on the other hand, allows them to adjust schedules, re-prioritize incoming assignments, or communicate back to stakeholders that things are slipping due to resource constraints (hopefully getting additional resources in the process). Communicating this to your manager early is also important, as your manager will have more options to make adjustments if the deadline for an assignment is months away, as opposed to weeks, days, or mere hours away.
How to get help and keep everyone's pride intact
Asking your manager for assistance does not need to be anything large or formal, it can be as simple as something like:
I know that D is coming up, but I am still in the middle of A, B, and C. Which of these should be my top priority?
I'm currently working on A, B, and C, but with D coming up I was wondering whether I should put A, B, and C on the back burner to focus on D. What would you recommend?
This phrasing communicates what you currently have on your plate, that you are aware of upcoming assignments, and requests the appropriate input from your manager. You are not declaring that you are unwilling to do the work, you are not accusing your manager of overloading you with work, but you are asking for feedback on your intended prioritization. It is usually part of your manager's duties to prioritize the tasks that you work on, so this should be perfectly normal and not have anything to do with your pride.
This answer on how to determine the urgency of a work request has some more recommendations on how to work with your manager on getting incoming assignments prioritized appropriately.