What antibiotic are you using? Penicillin is usually given in the breast muscle, Tylan can be under the skin on the back of the neck or in the breast muscle. Though some say in the thigh, the state vet told me that folks should never do that because they often hit nerves and can paralyze the bird.
Can't type much, carpal tunnel, but push into the skin, maybe 1/8" into the muscle, then slowly push in the plunger. You may need someone else to hold the bird.