Im measuring my blood pressure cause i'm query hypertension, but my initial number is always high (i have anxiety so i always check again) and the next two measurements are lower and lower again.. is this normal?

This is called the alerting response as squeezing your arm is sensed as something that may need you to flee or fight. So BP goes up just in case. Then body changes it mind and adapts. I recommend you take BP every min till it stops going down the take 3 more readings and average those. Take same time of day and use exactly the right sized cuff, positioning etc. Can also have Dr do 24 hr BP.