IMHO she was clearly lying. If she was mad enough to slap Riona when the topic of their shortage first came up, there's no reason she wouldn't have called Riona on creating the mess in the first place. The real question is WHY she was lying. Either Quinn herself still doesn't know why she's short and just needed an excuse to convince Tommy everything was fine, or Quinn knows the truth would only piss Tommy off even more.
Personally, I find the second scenario far more likely; if Quinn was still in the dark, I would expect her to put more effort into learning why. You'd also think she'd want Tommy's help in that endeavor, since her reaction when Tommy storms out shows she did not expect him to abandon her. Whereas I can think of several reasons Quinn might be short that she wouldn't want to reveal to Tommy when he's already angry.
My money is on Quinn being the one using without paying. It fits her use of 'powerful' drugs (the injection or the joint on the roof), and is one of the classic pitfalls for dealers who use their own product.
I'll admit I'm predisposed not to give Quinn the benefit of the doubt, but I think you're leaving out the other half of the equation. None of the other When Quinn tries to fuck the MC during the CUM-petition, Riona has no reaction. While Tommy is surprised if the MC fucks Quinn, the other DIKs are not. If the MC tells Melanie and Sarah, they are mostly just amused. Even the hyper-expensive threesome is presented as a chance to do extra-naughty things with Riona rather than as a rare chance to get a piece of 'queen bitch' tail.
So while I agree Quinn isn't sleeping around the way Arieth is, sex with her doesn't seem particularly notable, either.
Given that Bella is happy to serve wine to the MC (who she knows is a freshman), I don't think we can use that as proof the Jill is 21. She could be, but it's more likely she'll turn 21 at some point during the school year.