If doxycycline causes increase in intracranial pressure, will stoping the medicine stop the hypertension?

Yes it may but...: Pseudotumor cerebri is a clinical syndrome resembling brain tumors and is characterized by increased intracranial pressure. A number of conditions are known to cause the syndrome: metabolic disorders including obesity, prolonged steroid use, oral contraceptives; drugs including doxy-, minocycline; hematologic disorders including polycythemia and hemolytic and iron deficiency anemia.

Maybe, maybe not: The syndrome of pseuotumor cerebri is not well understood, and the doxycycline may be the extra item to bring out the full syndrome. Underlying obesity, hormonal issues, cerebral vein blockage, or endocrine issues may have already been present, and may well need sorting out. Would recommend further evaluation, trial of medication, and patience. Hope this stabilizes.