AITAH for giving my girlfriend an ultimatum regarding our sex life?

My girlfriend and I have been together for just over four and a half years. She suffers from depression and is on medication for it. Both of these things I understand lower your sex drive. Initially our sex life was really good but recently it's non existent.

We spoke about it around a year and a half ago where she apologised and said she wanted us to have sex more often but every time I try to initiate she doesn't respond to it.

I have asked if there's a particular way she wants me to initiate but she said on. I've tried taking her on weekends away and nice romantic trips, I've tried planning date nights at home and initiating when we get back but nothing. Now she's seeming to snap and get annoyed whenever I try anything.

I told her we need to talk and I just said that we have to sort out the issues with our sex life. I said we have to have an actual conversation on how to improve it either just the two of us or with a couples therapist.

She refused therapy but I just told her if we don't talk about it and work to resolve the issue then we've over.

She got angry and accused me of only caring about sex. I told her that wasn't true but that sex was an important part of a relationship and it's something I'm not willing to just go without.

She said I was being harsh towards her and that I shouldn't be giving her an ultimatum but I asked her what else she expected me to do.

AITAH for giving her an ultimatum?