I think it's definitely worth reaching out to your T in this situation. If you're unsure of her email policy, you could just write something brief, like, the first couple sentences of your post (and include the fact that you contacted the crisis line and that they suggested you contact her). If you wanted, you could say you were considering asking for an extra session and ask about her availability, too.

I've emailed mine numerous times between sessions if I've been struggling, and he always sends some sort of reply, generally in the morning. He's helped provide some support (even just knowing he'll reply in the morning has helped me get through a difficult night). I've also asked for earlier or extra sessions, which he has usually been able to give me. A few times, he didn't have space in his schedule, but once, when he realized it was a crisis, he added an extra session at the end of his day to meet with me. Another time, he had a last-minute virtual session with me in the evening (but this was unusual for him).

Mine made his email and texting policy clear from the beginning, and we've discussed it throughout the time I've been seeing him (4 years). And he's said from the beginning, too, that I can always ask for an extra session. I'm not sure what your T has or hasn't said to you about this, but I think a brief email is fine. And you can even say, "I hope it's OK that I'm emailing." I imagine your T would want to know that you're struggling.

Also, if you think you might want an extra session, it's probably best to come right out an ask for one. I know some T's might go ahead and offer, but for mine, I have to specifically ask.