Juat injecting him would involve hand to hand combat and Max is a bit of a weed. What you need is some sort of ranged weapon Exchanging objects with Nina is necessary for this.
More specifically
Spoiler:The leg of the chair in Nina's cell
To get that you'll need to
Spoiler:Pass Nina the scalpel
Then you can
Spoiler:Use the leg, the syringe and the PCP to make a blowgun.
Advanced warning, there is a bug in this section of the game that affects some people. At some point in this section you'll trap an animal. If you still can't pick it up once you've trapped it (no hotspot for it) then you'll need to install
this patch.