10,000 feet is not very high. Most likely the headache you were experiencing was due to some combination of sleep deprivation, caffeine withdrawal, and unaccustomed exertion and aerobic challenge. It would be unusual to experience any discomfort whatsoever at that altitude. Most people don't need any acclimatization for that altitude. I've hiked with a lot of people on day hikes up to 10,000-11,000' in the Transverse Ranges of Southern California, and very few had even a headache. For comparison, La Paz, Bolivia, is at 12,000', and people don't keel over and die when they fly into La Paz from sea level.
At altitudes more like 12,000 to 14,000', it's more common for people to start to have discomfort (nothing life-threatening) due to pH imbalance in their blood. If you're going to these altitudes without acclimatization, or even higher altitudes with acclimatization, you may want to consider getting a prescription for diamox (acetazolamide), which helps to rebalance your blood pH.
Should I be worried when I get a headache due to altitude change?
No, not at 10,000', if "worried" means worried about dying. Of course, if you feel lousy, you feel lousy. You're not having fun. That could be a good reason to reconsider your options, such as turning around or waiting somewhere while your companions summit and then pick you up on the way back.
What are the signs I should be watching out for, if not headaches?
Wikipedia lists the following symptoms of high-altitude pulmonary edema (HAPE): "Symptoms: at least two of:
Difficulty in breathing (dyspnea) at rest
Weakness or decreased exercise performance
Chest tightness or congestion
Signs: at least two of:
Crackles or wheezing (while breathing) in at least one lung field
Central cyanosis (blue skin color)
Tachypnea (rapid shallow breathing)
Tachycardia (rapid heart rate)."