What are the stress levels a software engineer experiences?

I get this is probably a situational question. I'd imagine when working for an existing company, there are certain deadlines you have to meet to get stuff done and expectations are higher. Does this change at all if you are developer working with a start-up company instead?

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The reason why I ask is that I'm thinking of declaring software engineering as my major since starting my own independent development project in Python. I have an autoimmune condition and the amount of stress I'm under directly impacts how I feel physically and mentally. If I'm pressured into meeting deadlines constantly, then I'll probably absorb less information and feel like like junk all the time– which something I've already currently encountered with school/work. Part of going to school is not to do something that genuinely interests me, but also to gain a more comfortable work-life balance and lifestyle.

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Does software engineering fit this criteria?