Would an echocardiogram and stress test show if there was a blockage or problem in the carotid arteries?

No. U need bilateral carotid ultrasound study to evaluate carotid artery disease or blockage. An echocardiogram will evaluate functional and structural anatomy of the heart, while a stress test show the functional capacity of the heart.
No. Echocardiograms & stress tests are used to evaluate your heart's function and possibility of blockage in arteries to heart. However, neither test will evaluate carotid arteries. At your age, given your gender, you shouldn't need either test, nor to worry about stroke risk, unless you have an extremely strong family history of premature heart disease & stroke. Carotid ultrasound will check nec.

Related Questions

Why would I see the vein sticking out only on left side of neck? Normal EKG, stress test and echocardiogram in Feb. And normal u/s of carotids in April.

Vein. A vein sticking out can be from anatomic means like a nearby artery pushing on the vein and causing back pressure. If your doc has examined you and finds nothing to worry about, it is likely some internal insignificant partial obstruction. Since you've had so many studies, your Doc should be able to advise you. Read more...
It can be. normal to have asymmetry in size of the jugular veins. However, if this represents a change from your normal appearance, see your doctor, because it could be a sign of obstructed venous flow. This would be very unlikely if you have no other symptoms, however. Read more...