It would be "the doctor gave me an infusion".  This only applies if something is provided directly into the veins like through a drip feed.

For something that is administered beneath the skin into fat or muscle, for example insulin or a vaccine, you would call that an injection.

https://www.youtube.com/watch?v=HbhvZ2y1V80

"Transfusion" by Nervous Norvus

http://www.oldielyrics.com/lyrics/nervous_norvus/transfusion.html

ZZZZZZOOOOOOOOOOOOMMMMMMMMMMMM
Tooling down the hightway doing 79
I'm a twin pipe papa and I'm feelin fine
Hey man dig that was that a red stop sign
[Scrreeech-BANG, tinkle]
Transfusion, transfusion
I'm just a solid mess of contusions
Never, never, never gonna speed again
Slip the blood to me, Bud

.

.

I jump in my rod about a quarter to nine
I gotta make a date with that chick of mine
I cross the center line man you gotta make time-
[Scrreeech-BANG, tinkle]
Transfusion, transfusion
Oh, man, I got the cotton pickin convolutions
Never, never, never gonna speed again
Shoot the juice to me, Bruce
.

.

My foot's on the throttle and it's made of lead
But I'm a fast ridding daddy with a real cool head
I'ma gonna pass a truck on the hill ahead-
[Scrreeech-BANG, tinkle]
Transfusion, transfusion
My red corpsuckles (sic) are in mass confusion
Never, never, never gonna speed again
Pass the crimson to me, Jimson
.

.

I took a little drink and I'm feelin right
I can fly right over everything everything in sight
There's a slow poking cat I'm gonna pass him on the right
[Scrreeech-BANG, tinkle]
Transfusion, transfusion
I'm a real gone paleface and that's no illusion
I'ma never never never gonna speed again
Pass the claret to me, Barrett

(continued)
.

I would say the doctor gave me a transfusion.  The fact that the bottle is drip - feeding the serum into the body is understood.    This means the same, but is more formal  " The doctor administered a transfusion to me.   That is in the passive voice which most English speakers do not use.  The first example (active voice) is much more common.