Is it possible that my blood pressure is still the same?

After 2 years of not seeing a doctor (never sick and at the time did not have health insurance for a regular checkup) I visited a doctor for the first time and was told I had High Blood pressure. My pressure was taken twice and was 136/108 and 138/100. I was told I should try to change my diet, try to lose some weight and come back for a follow up in 1 month. My diet was very unhealthy, I was inactive and usually had 3000+ mg sodium a day with caffeine and moderate alcohol use.

In one month I lost 10 pounds and and kept my sodium intake under 2000mg a day, usually between 1500-1700mg a day. I also began doing 30min-1hr cardio, 3 times a week. After going for my follow up, my blood pressure was again taken twice and the numbers were 130/102 and 138/102. Now I am being prescribed medication. Is it possible that my blood pressure is still the same considering the large change in my diet, and add of exercise? Also, does this prescription make sense? I am worried about taking medication.