hypodermic
it. 
there is
me.

Looking in The Evolution of Anaesthesia by M.H. Armstrong Davison
(pub Williams & Wilkins, Baltimore 1965) I found the following
chronology:

"1853.  Charles-Gabriel Pravaz (1791-1853), inventor of the
galvanocautery, describes a glass syringe with tapered nozzle. This
syringe was intended to be used with a special trocar for injecting
ferric chloride into aneurysms, and thus to heal them by coagulation.

1853.  Alexander Wood (1817-84)  of Edinburgh invents the hypodermic
needle and adapts Pravaz's syringe for use with it."

You might also be interested to read about the experiments of Sir
Christopher Wren in 1656, described by Oldenberg & Clarck in the
Philosophical transactions of the Royal Society in 1665. Using a
sharpened quill and a pig's bladder he injected opium, wine and beer
into the veins of dogs.