You should only be administering antibiotics under the guidance of your vet and they should make the method of administration clear to you. Some drugs are potentially very dangerous if administered the wrong way.
some drugs are administered into the muscle and some orally, depends on the type. Horse drugs are not administered sub-cutaneously (under the skin) as there are no areas of horses skin that you can 'lift up' to be able to inject under the skin. If you are administering into the muscle (ONLY a vet can administer into the vein or somebody under the direct supervision of the vet, and even then it must be a set dose rather than a dose that is delivered depending on the reaction of the animal) then once the needle is in, you MUST draw back on the syringe to ensure you dont get any blood back. If you get blood in the hub of the needle, you must remove the needle and choose another site for injection, again, draw back to ensure there is no blood. Do not worry if after the injection (once you have removed the needle) there is a little bleeding from the injection site, it just means you've hit a little vessel in the skin, as long as you get no blood back in the hub of the needle, you are ok to inject. your vet will show you sites where you can inject. Hope that helps! Not all drugs that can be injected are available as oral administration and vice versa, just depends on the type of antibiotic.
Some drugs are given subcutaneously to horses. I had to give a subcutaneous injection to one a month ago.
Going back to the the posters case though, I would expect it to be IM. Choose the best site that works for you, make sure you are shown how to do it properly by your vet and if you don't understand any part of it, please make sure to ask.
my vet told me to give a 3 day course of pennicillin to my TB subcu, i gave it to him by pinching a fold of skin in his neck and i could lift his skin no problem...he just about killed me on the 3rd day as he knew what was coming though!
when you were piching the skin at the neck, it will have been going into the muscle. if injecting in the neck you do pinch the skin but the needles used (1inch or 1 1/2 inch) are too long to just go under the skin. You would need a very short needle (5/8") to only go under the skin. if you were using penstrep (a penicillin brand name), it will have been into the muscle.