250lbs at 5'10" is very overweight. That calculates out to a BMI if 35.9, which is clinically considered obese. However, football players (mostly linebackers) can be this weight and be very healthy because most of it is muscle. Although they are also a couple inches taller.
Your doctor can order up bloodwork to check cholesterol, liver function, etc. to measure your overall health and check for risk factors or heart disease. And I would assume he or she would also have told you if you blood pressure was too high.
The best way to determine how much of your weight is actual fat is to get your body fat percentage measured. You can sort of do this at home, but it's you'd get a more accurate number of you ask your doctor about it.
Body fat percentage - Wikipedia, the free encyclopedia