Hello. By broken vessels I presume you are talking about the redness caused by bleeding on the surface of the eye. This is called as sub conjunctival haemorrhage. These are not per se harmful except that they might be cosmetically unacceptable. They usually resolve without any sequelae. Taking vitamin c tablets or lemon juice 4 to 5 times a day is equally effective. Omega 3 fatty acids (after consultation with your general physician / family doctor) Now coming to your second question. These red eyes when associated with hypertension indicate an on going internal damage to your eyes and other internal organs. This might be at an initial stage as well. So I suggest that you get yourself checked at the earliest by an ophthalmologist and get a bas line value for your eye status. This will help in determining your current disease status and also serve as a control for monitoring disease response or progression. Hypertension requires a periodic checkup every 6 months with your ophthalmologist. Hope this answers your queries.