Here's an answer without claiming it's extraordinarily Buddhist.
Buddhism might recommend you be resistant to (or perhaps transparent to) blame and censure.
From two traditions:
I think they're also called "eight winds" -- so just let the wind blow through you, as it were, or don't be there for the wind to blow on, might be my advice to you based on my small experience of it.
And the fart is a related story -- trying to explain not being moved by reputation -- though possibly harsh.
That's not to say that you "don't care" -- I think we're warned that people who are "incapable" of remorse will tend towards being ill-behaved.
I think you're supposed to accept the teaching of your teacher perhaps (and/or "spiritual friends"), but perhaps you might be a better judge of your own character and intentions than other people are.
If you want to avoid being gaslit then perhaps "remembering your own virtue" then is important. And then again in this story -- Is That So? -- the question of "Am I the one to blame?" was not the important question.
Another doctrine is that "skilful virtue" on our part should occasion "lack of remorse" and, from there, some joy -- a "lack of remorse" (though not "incapable of remorse") is perhaps a good "defence" against being gas-lit -- except that perhaps it's not a defence (an ego-defence), in the sense that some absence of remorse is non-existent (see e.g. this topic).
People attempt to blame or appear to gaslight "me" on this site, sometimes, I could reference comments as examples. It might help to see that as neither true (it isn't a brilliant description) nor false (they are really saying that at the moment), it's perhaps their "view"? Whether it's even a semi-accurate view is another story, your saying "gaslighting" implies you think it isn't accurate.
But communication problems exist between people. And what people say -- e.g. about relationships and how they perceive you -- might also be based on something like their own experience with their own family and society ... so it isn't always easy to agree with everyone and about everything, and of course people might reach different conclusions when they start from different premises, and when egos become involved.
As for your gaslighting other people I'm not sure why you think you are or want to be doing that at all. It might perhaps be typical of the competitions which people get into -- like "I am superior to you", or, "I am more deserving", see also this answer (about "conceit" and identity view) -- and a reason to be careful of what relationships and personal relationships you engage with -- see also Any authentic sutta from any tradition that gives guidance on what kind of partner to choose?
For more on whether you're gaslighting people try to pay attention to right speech and to not being a sectarian.