No more than 10 ccs should ever be given IM at one site. If you are going to be giving more than one dose, then you have to rotate your injection sites. Penicillin really should not be administered into the neck muscle as it is too thin. The semitendinosus muscle below the point of the buttock is the best site since the muscle is large, the drug will be dispersed as the horse walks around, and if an abscess or hematoma forms, it can drain well in this location. There is also less risk of hitting major vessels or nerves.
When you prepare penicillin suspension, it should be warmed to room temperature and shaken thoroughly before you draw it up. Insert the needle straight in perpendicular to the skin surface to assure getting deep into the muscle, then attach the syringe and aspirate for blood. If any enters the syringe, remove the needle and apply pressure over the site until bleeding is completely stopped. The needle should be discarded into the appropriate container and Ideally you should discard the suspension that has been mixed with the blood and start from scratch. At minimum, be sure to use a new sterile needle, and don't reinject with the same contaminated one.
Be sure you have the right gauge and length of needle for IM penicillin injection. Penicillin has a high concentration of suspended material which can clog the needle if injected too rapidly, so inject it slowly and steadily.
If you still decide to use the neck site, only give one injection on each side of the neck and the rest of the shots have to go into other sites. Again though, it is best not to give penicillin in the neck.
Hopefully your vet gave you epinephrine to have ready in case there is an anaphylactic reaction. Anaphylaxis usually occurs within a half hour after the injection, so be sure to observe for it. If you don't have epi on hand, giving the shot is risky, as reactions to penicillin and to procaine are fairly common, especially if your horse has any other known allergies. If that is the case, i'd have the vet come to show you how to use the buttock site, and to provide you with epinephrine and instructions on what to do in case a reaction occurs.
Here is a link with photos of injection sites you can scroll down to. The one I recommend is at the rear below the point of the buttock.
http://www.aces.edu/pubs/docs/A/ANR-1018/
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Add........... If you do choose the neck site, do not "find a fatty area" on the neck as is being advised in another post. Be sure you use the location pictured in the link I posted, and not above or below it, staying at the base of the neck. This shot should be administered deep IM, meaning it the penicillin is delivered deep into the muscle, which means you don't want excessive fat overlying your IM injection site.
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Add ............... Administration of an IM injection of more than 5 ccs of penicillin into the thin muscle of the horse's neck is not advisable, despite the fact that many vets choose the site for ease of administration just as some human medical professionals still choose to inject penicillin into the deltoid muscle (at the patient's expense) as a matter of convenience while knowing it is not the preferred site. The neck site can be used, but choosing it does not serve the best interest of the horse. Many of us who administer hundreds of these injections on a weekly basis choose to use the Z track injection method in the largest muscle available on a given patient in order to avoid leakage of penicillin through the needle tract because of the associated high incidence of reactions and tissue damage. Just because you can use a site doesn't mean that you should use it.