Not all deadlines are detrimental to your mental and physical health. Deadlines can be good too, you know. How? You ask. There are a ways to ensure you get the job done and don't lose your mind during this while:
Set effective deadlines: Learn from past experience (if this is your past time on that particular project, ask around) and know average time frames for each task, sub-task and so on.
Basically, act like the project manager of you, inc.