I texted my therapist once when I was in a crisis but there was no fixed session ahead (she had left it open-ended because she thought I was better). Other than that, I am very uncomfortable seeking her out first because I feel like she will find me needy/annoying/attention-seeking. So basically she almost always texts me first, either to confirm appointment timings or to check on me, though sometimes she does not reply me

I know this is because she is off-work as she knocks off at about 5.30 p.m. but it hurts me a little to know that I'm considered as "work" and can never be close to her the way her family is (lucky people!!) For example last Fri she texted me to see how I was doing (as I was feeling suicidal) and I replied saying no, but my hallucinations were getting worse, and she asked how that made me feel, after which she did not reply (about 6 p.m.). And of course, I didn't hear from her over the weekend.
Haha I get what you mean by the problems w.r.t. texting/emailing. This is why I don't don't email and only text when she does. It mostly has to do with my intense dislike of neediness (though I do need her more than words can describe) but also because she has never explicitly said that I could call and I didn't want to catch her in a meeting/lunch or session with another client.