Be around them, buy some at a pharmacy and learn to look at it as innocuous. Then train your mind to never visualize a deep stick, it almost never happens anyway. Needles are generally less than an inch deep. IV's or blood donations the needle may look long because it goes in the vein but it's generally less than a qtr inch deep. So see it for what it is; a small object making a nominal puncture.
That helped my dad, plus I called him a sissy pretty relentlessly to make him give in and get his blood work done. When they told him what all needed to be addressed that the blood test found he began to see the value of the shots.
Oh, one final thought: I was in the Marines. Rarely used needles, they have the thing that blows it in thru the skin. So you might not get as many shots as you are worrying about.