I worked at the hospital in Vail (8150 ft) for several years, and can say that what you're feeling is perfectly normal. Acute Mountain Sickness (AMS)can be very mild for some and life threatening for others. We would often see folks who have been coming to the mountains for years but "never felt this way until this trip," then would be fine the next time they came out. AMS can be pretty unpredictable. I've noticed that some people seem more vulnerable when there's a low pressure weather system over the mountains but I have no factual data to back that up.
Physiologically, most people get used to the symptoms (shortness of breath, rapid heart/respiratory rates) in a few days; it takes your body about 3 months to fully adapt but some people never do get used to it.
What helps? Hydrate, hydrate, hydrate. If you can, stay at a more moderate altitude at the start of your vacation, then work your way higher. Don't exert yourself greatly for a day or so, and watch the alcohol. Some people benefit from a medication called Diamox starting a few days before coming to altitude, your doctor would need to prescribe that for you.
Danger signs to watch for include coughing up reddish froth or extreme confusion. Pink froth from your lungs is a sign of high altitude pulmonary edema and you'll need to get to an emergency room. Sudden confusion can (doesn't always) be a sign of high altitude cerebral edema, which is quite rare but a true medical emergency.
Not to worry you, most people feel a little winded for a few days and are just fine. By the time you read this you'll probably be feeling better already.