Yep. Been there. I had a horrible phobia of needles, too.
First off, know that once you get past this shot or series of shots, you may not need to get any more for years to come. Maybe decades.
Secondly, keep in mind that shots don't hurt as much as drawing blood does. If your fear is based on a bad experience with drawing blood, then it's understandable that shots could seem intimidating. But aside from a few shots (like tetanus shots, or the MMR shot) most of them are just a quick prick, and no real pain.
Also keep in mind that the more stressed out you are, the harder it is to 'find a vein'. Some people just have harder-to-locate veins, and thus bad experiences with nurses pricking them over and over again. Which sucks. If you're relaxed, the vein is easier to find. Also, if you're relaxed, your muscles don't tense up, and so you won't feel as much pain.
As a last desperate measure, you can ask your doctor for topical lidocaine. It's a chemical that numbs the skin in any area. It may cost some money on the medical bill, but just call and ask them if that's something they can do. If so, then you'll quite literally not feel the needle at all.
But most importantly, don't be scared to watch. People would always tell me not to look, and that would make it worse. Go ahead and watch. It's your body, and your right to see what happens. It's not all that exciting, but it's less stressful than being told you can't watch. And don't be scared to tell the doctor/nurse administering the shot that you're a bit scared of needles. They deal with it all the time.
Good luck. Hope this helps!