Your headache means you're overloading yourself, most commonly it's caused by too little sleep. Your body is telling you to chill for a day and by silencing it and continuing living the way you do, you risk getting something systemic.
When you have an infection, fever boosts your immune system. Block this and risk a complication. Surely, the risk is low while you're young and healthy, but it's not zero.
The only legitimate reasons to take NSAIDs are post-surgery treatment and arthritis.
My advice to OP: next time you break a leg, take however much ibuprofen you need not to feel the pain and keep walking.
I'm not young, but I've been experiencing migraines since college. I do pretty much follow this advice though. Last time I had an actual fever, it was around 102 - 103F for three days, but I didn't do anything except fluids and rest, and called into work, of course.
It's also accurate that I push myself and I force myself to work even when I've barely slept, but that's the nature of my work. Lots of people rely on my assistance, and I don't mean my boss or co-workers. Still, best job I've had in my lifetime, and I've been around a while.
It's been months since I've had a migraine, and I've noticed it happens less since I learned I have celiac and made the appropriate adjustments to my diet. But when the migraines hit, there's no ignoring the pain. Incapacitating, excruciating pain. To the point that sticking a knife in my temple seems like it would provide relief.
I'm not even sure the ibuprofen helps under those circumstances, but I get desperate. Sometimes green tea or coffee help if I catch them right at the onset.
I will take your advice to heart though. I'm willing to improve my life in whatever way I can.