What are some exercises that do not require a lot of movement?

I am trying to lose weight, but I was diagnosed with high blood pressure. My doctor said that I cannot get overheated because that will make my blood pressure rise. I tried to go for a walk, and after a mile, I got overheated, and I started feeling really dizzy. My husband had to help me home, and it took hours to go away. All I drink is water, so I stay very hydrated.