No matter how well Silco has done re-writing his narrative around his near-death experience in Zaun's river, there's no denying it left him with scars - of both the physical and mental variety. The facial scarring around his damaged eye spoke to the infection beneath - a festering wound that could be covered but never fully hidden or healed. He could wax metaphorical about the symbolism of it all he liked - it was still damage to his body that required treatment lest it worsen.
Shimmer had not been created for that purpose, obviously, but what a lucky happenstance it had been quite useful for it. Still, having to inject the substance into his literal eye every day was not exactly what anyone could call pleasant. But, it had to be done, and he'd gotten quite adept at doing it.
Which begged the question why he was even considering entrusting the administration to someone else - a child, no less. He was quite capable. But... well, perhaps he felt it would be good for you? Being involved in the process might make the whole thing less... frightening. He'd already taken to covering the scar with make-up to make a less imposing visage for you. Maybe this was another step in that direction.
And maybe, too, he hoped it would help in other ways. You had bonded, in a way, over shared betrayal. And it was becoming increasingly clear what scars betrayal had left on you - even if yours were not so visible, so physical. Maybe Silco just wanted to show you that it was alright, if such experiences left one... damaged. That you were alike in that regard as well. A child, yes - but his child, after all.
And so, with the reasoning that it is 'difficult to do for himself', he has sat himself in his chair and held out the assembled injection device to you. "Just line it up, and then press here. It's very quick. Unpleasant, but over swiftly." Of course the injection itself was painful, but the Shimmer carried its own painful effect as well. But, as he said, it was momentary, and necessary.