Irrational fear of needles and shots- can a kid overcome it?

Yes: Yes they can overcome fear on needles. I did, well, not as a kid. During medical school. Be supportive of your kid. Talk to him, rub his head/back when getting blood draws, do happy talk. This will distract him (sometimes it works, sometimes it does not).

CBT: Seek a cognitive-behavioral therapist who specializes in phobias. One method they use is systematic desensitization which slowly and incrementally brings the person closer and closer to the thing they are afraid of in slow, graduated steps that help make the anxiety more tolerable.

VRT for Phobias: Phobias and anxieties respond well to Virtual Reality Therapy(VRT). VRT is exposure therapy in a safe environment. The research suggests VRT is 90% effective. Seek out a therapist who uses VRT in your area. You can find providers through www.psious.com, www.limbix.com, or www.virtuallybetter.com.