One thing I found helpful in times when there are multiple urgent requests on a project, is to look at the current status of the project and look for buffer hours for each task. Next is to create a list of requests and see if any of those tasks are part of scope of work and are doable in the current sprint.if yes prioritise those tasks and move lower priority tasks to the next sprint after discussion with stakeholders in the project. Now for the tasks that are high priority but not a part of Scope of work are to be discussed with stakeholders and be sure to be ready with the rough estimates of all he tasks so stakeholders can be aware about how long the task will take if started with current sprint and doesn't affect any ongoing tasks.

Setting aside time where you won't be interrupted is critical for working on these tasks. Make sure your calendar is blocked, notifications are off, and your DND is on. Door closed, etc. Take a little time to assess your priorities - look at what's important first, and rank those by urgency. Break them down into smaller chunks so you can accomplish the overall task one piece at a time - this will help manage the stress.