Sir it seems your mom is having problems in the neck Your mothers Bp has to be taken atleast three times both in lying and sitting position to confirm she is hypertensive if her Bp is more than 140 /90 it is better to have life style changes  with low dose antihypertensives like Amlong 2.5 mg once a day mean while check her blood sugar fasting and post prandiallipid profile EcG Hb percent For life style changes she should she should not give strain to neck can have a cervical pillow and use intermittently cervical color if x ray of her neck or mri show changes in the neck bones or discs can have physiotherapy and cervical exercises once vertigo is controlled as you have said salt restriction fat restriction could be tried weight reduction could be tried as she is having dizziness walking has to be done with caution eat more of vegetables and fruits if her blood sugar is normal ask her to sit or lie down immediately if she feels giddy with support from near by

Kindly discuss for your concern

First check regularly bp at home. 3 times a day for 7 days. Share the readings. Do regular exercises and yoga, diet and lifestyle modifications. If BP remains above 140/90 then need to start proper medications