Is beta blockers is adequate treatment for spikes in blood pressure due to prolong stress?

Impossible to answer: because wrong focus. Stress=a vague, complex, catchall, poorly defined concept stemming from complex mental perceptions, expressed via brain into body in a huge number of poorly understood, poorly quantifiable ways. Beta blockers are just molecules which emulate adrenalin/noradrenalin, without stimulating receptors; competing with these hormones reaching receptors for them. Study my other answers.

Maybe: There are a variety of BP meds, often used in combinations. The answer to your question is to record numerous blood pressure readings over many days and at different times. You must have a home BP kit, one on the upper arm, not the wrist. Beta blockers are very useful. As single agents, they are the least effective of the BP meds. You will know how effective with multiple BP measurements.