Altitude sickness is very real, and can be very dangerous. Nausea, shortness of breath, rapid heart rate, and headaches are other symptoms to be aware of. Frequent recommendation is to get to a lower elevation until one acclimates to the change in altitude. And hydrate...hydrate...hydrate.
Even those of us who have lived at a higher elevation can experience altitude sickness. I have had issues going up to the top of Mt Evans (14000 ft), as well as several points along Trail Ridge Road (at 12000 ft) at various times. Doesn't happen every time. I've also gone up Pikes Peak on the cog railway and didn't have any problems at the top.
Most folks can acclimate to a change in altitude. It may need to be done gradually. Not everyone is going to respond the same way. Much depends also on your age, general health, and general physical condition.
Worst thing to do? Ignore the symptoms.