People who take analgesics regularly for headaches can actually (for lack of a more medically accurate description) make themselves immune to analgesics. So that's one thing.
Another thing is a fever medication isn't necessarily right for a headache anyway.
Headaches can be caused by all kinds of things, and - really - if a headache persists, a person should see a doctor (to at least get checked out). If your headache is caused by sinus congestion (and that doesn't have to mean having a stuffy nose at all, but instead may cause you to feel from vaguely cloudy-headed to clearly "blocked") what you would need would be to clear your sinuses. It can be caused by tension (try relaxing every last little muscle you have from your shoulder on up to your scalp). Sleeping wrong can cause it. If it's a migraine (which is a special kind of headache with a specific set of symptoms and a pattern of coming on and leaving) you could get some help from a doctor. Aspirin doesn't help caffeine-withdrawal headaches (which, of course, occur if you drink/eat a lot of stuff with caffeine in it; and then suddenly stop or drastically reduce the amount of caffeine). A caffeine withdrawal headache may die down if you drink a couple of cups of coffee or tea.
Not getting enough sleep can make you have a headache. So can low blood sugar. In any case, stop taking whatever you've been taking (if you've been taking quite a bit of it). Be careful not to take any aspirin with caffeine in it. If this is only one headache episode (and you haven't made a habit of using analgesics before now) you could try either ibuprofen or acetaminophen. They are different from aspirin. Neither should be taken for too long. You could try putting a cold compress on your head, or making sure you get out and get some fresh air. If you think it's caffeine withdrawal or low blood sugar, a cold glass of cola might help either of those.
Other than that, if you have a headache that won't go away - again - you really should see a doctor. It could be something that requires immediate medical attention. If nothing else, a doctor would probably be able to suggest/prescribe a medication (and a dose) that would be more effective than OTC headache remedies.