I feel very similar to you OP, I obsess when ANYONE I feel matters to me doesn't reply to something I've sent...I assume its my fault

My T does allow texting and email as well but I've made my own boundaries on it. Like I wont email more than 1x a week unless he asks for something. (I have actually gone almost 3 weeks with no email even) and I text but no more than 2x a week and it's usually brief like about if I am still coming to session or not etc.

I know if I was doing it often either one, my obsessive thoughts would get worse even though he has no limits on them for me.

It's hard but just try journalling or finding another way to clear your mind of it, like tv or talking to a friend etc... usually when there is no answer form my T, which is rare but it scares me, it ends up being a good reason when we discuss it.

If you need the reassurance it's ok to still email/text as often as you do, ask. If you need to know if you are becoming "too much" ask. I do often and he has no problem reassuring me

Good luck