LBBB (Left bundle branch block) is an ECG abnormality of conduction system of the heart. It necessarily does not mean heart disease. The elevated BP that day may not be related to this. LBBB in your case might have been pre existent. At times it is intermittent, appearing with faster heart rates as during anxiety or exercise etc.
Presence of LBBB however needs a work up to rule out underlying heart disease. An echocardiography is one of the tests, which you must undergo. It will reveal any weakness of the heart muscle. A 24 hours ECG monitoring (Holter monitoring) to look for any intermittent abnormality of heart beat like a very slow rate or fast rate is also a relevant test. Besides this blood biochemistry to diagnose any diabetes, kidney function tests and evaluation of cholesterol and triglycerides is desirable. Based upon this evaluation, more detailed tests, if necessary can be done.
There is no particular medicine to treat LBBB. The treatment is directed against any underlying problem. If everything turns out as normal then only an annual ECG is advised.