This is the reason women have higher voices than men. The vocal cords are smaller and vibrate faster producing a higher pitch. Whatever your voice type may be, you will have an upper and lower range. When the cords are vibrating slower you are using your lower range and visa versa. In order to sing higher, the cords must vibrate faster.
Air is the main ingredient to producing a singing tone.
See lesson 2 of Voice Lessons with Dave and Shalee . It has many great exercises to increase your breathing ability. Tension and pressure are not needed to produce high notes. Use your best breath control and vibrate the cords faster. Practice every day.