I understand very well what you are talking about. When I was very young, I also experienced a very painful procedure, when a nurse several times could not get into a vein.
Since then I have become afraid. And it so happened that after 18 years I needed to regularly monitor the level of hormones in the blood, and this is done through the study of venous blood.
What I recommend to you:
1). Don't be afraid to ask for a thinner needle. I rent about once every 20 days and always ask the nurse to use a needle for very young children. It turns out almost painless.
2). Find "your" laboratory. This is useful if you have to go through a similar procedure regularly. Again, from personal experience - I have been going to the same laboratory for four years, therefore the attitude to the “regular customer” is special there.
3). Drink some water before testing.
4) As noted above, it is better not to watch everything that happens 😄
Dear Anna! Initially, you need to tune in to understanding the speed, painlessness and the need for this manipulation to carry out the examination assigned to you. In order to facilitate the collection of venous blood, you can perform this procedure lying down, not watching the venipuncture procedure, but view the information you are interested in on your phone, tablet, and other means of communication, and also invite one of your friends or relatives to as "support"