Many people have a fear of needles and this can make it difficult to have a shot. They can even become very uncomfortable around needles even if the procedure has nothing to do with them. Most times this fear results in a flight response as they want to get as far away as possible from that needle as possible.
Also some people may be fine with needles in one context while they may have a great fear of needles when they are used to take blood.
As with any phobia you need to try to understand what is the trigger to that phobia or if you can uncover what encounter caused your fear of needles. Some people may not have a problem with needles at the doctors but become paralyzed when going to the dentist.
Hypnotherapy can be a great way to treat your fear of needles. Chronic and long standing fear of needles can be successful to curing your fear of needles. This type of therapy uncovers what caused your fear, mainly a childhood experience and then giving you calming exercises to try when you start to panic.
You can also use behavioral therapy so that when you come into contact with a needle instead of getting flight response you instead have a different response that does not end with panic. You can also force yourself to do this. So when you encounter needles you take deep breathes or think of something else.
Many people all try to be able to be around needles more. If they have needles around and they are part of the background then it is not such of a surprise as they are used to being around needles. You may need support and someone to hold your hand when you first start but with support you can overcome this fear.