Clarify with your manager who is allowed to give you tasks. In a lot of environments, all requests from higher-up MUST go through your manager for prioritization. Make sure you know where and when this applies but it's probably most of the time, so just tell people "you need to go through my direct manager so we can track the things I need to work on". If you let four different people dump tasks on you, you'll get buried and you won't get your responsibilities done.
This bit me pretty hard my first few jobs and still does to some extent. Make sure you know what you're supposed to work on. If your plate is already full, don't branch out to other tasks. People are really good at overstating or understating the importance of what you need to work on, and you aren't the one who sets the schedule. It might be urgent for task A to get done this week, but maybe it's even more urgent for task B to get done by the end of next week, and if task B takes more work to get done...