As you now know, that is a very high reading...certainly could be the cause of the headaches. Yes, while your working out, your Blood pressure elevates but returns to normal after exercise. Exercise also reduces BP in the long run. I hope your staying away from all gear and stimulants...they'll just make things worse.
Diet and cardio exercise is a must, but with that degree of hypertension...they should do more testing to see why your BP is so high at your age. Yes, stress can certainly elevate BP but thats pretty high for stress alone. Purchase a home BP monitor and see if its less when you take it at home. Many people's BPs elevate when they go to the doctor's office.