stress test

i was recently in the hospital, my blood pressure was very high, and i was having pain in my chest and my back left shoulder after running every test except the stress test, they said they could find nothing at all wrong. just got my blood pressure regulated with medication, and sent me home.  the doctor however, still wants to run a stress test on me.
question: can a stress test reveal something that the other tests did not?
i just don't want to take unnecessary tests because of  the cost, but if i need it, then it's ok

[Encephalomalcia]

Because all the tests turned out okay, the stress test would be the next step to see when exercising if the blood is flowing through the heart properly.  It would be a good idea to have the stress test.  If you do not pass the stress test, they would know that something is wrong.