Hormonal birth control increases the chances that a blood clot will form in any women who takes one. In younger women the risk is low enough that it is seen as an acceptable price to pay for the many benefits of hormonal contraception
. As women get older, the risk does go up. At age 35, there is a rise in this risk, but most of the blood clots found are in women that smoke. Thus, the main group of women for which hormonal contraception is not given is women over the age of 35 who smoke.
Other examples of women that should not be on hormonal birth control include any women that has ever had a major blood clot, or those that have been found to have a blood clotting disorder. If neither of these describe you, and you do not smoke, then your doctor
will likely not have any problem prescribing you birth control pills.
I suggest that you schedule an appointment with your OBGYN. The two of you can discuss the pros and cons of hormonal birth control. Your doctor will also be able to provide you with statistics with your risk for a blood clot given you age and other risk factors. From there you can make a decision about what to do. Good luck.