The speaker pictures keeping their own body in a bottle, something to carry around, uncork, and talk to. It's a strange, funny image, but also a lonely one. Whoever is speaking needs company so badly that they turn themselves into it, splitting into a drinker and a drink, a listener and a voice.
The warmth of the third line works two ways. Drinking brings a literal glow, but the phrase "I drink myself warm" also suggests that the speaker is their own only source of comfort. Then comes the odd, slightly boastful final line: "I think myself a very pleasant present." The word play on "present" (a gift, and also being here, in the moment) gives the line a gentle charm, though it may be self-persuasion more than real confidence.
The mood is quietly playful on the surface and sad underneath. The title, "Self-medication," hints that this cheerfulness is a kind of remedy, and perhaps a fragile one.