I'm sorry you are feeling depressed and alone. And sorry too that your T is having challenging personal issues.

Please go ahead and contact her. She is a separate person and she gets to decide what she can deal with. Since she hasn't changed her offer of outside contact, then it is still in place until she does. And I'm sure she will understand you worries.

This is one reason some T's don't self-disclose. It can cause this kind of reaction that includes a fear of the T's capabilities (at this time) and can shift the focus of therapy from the client to the T.

My T has a busy life, travels a lot. Some of the travel I know about, other travel is to visit family in another state. She always lets me know if she is not going to be reachable and is otherwise reachable by phone or email. I email, and if it's a time I know she's busy, or it's a holiday, or traveling, then I try to keep my email as brief as I can. I'm sure though that there have been times she's busy/traveling/etc that I know nothing about so I just have to trust her. I've also asked a zillion times "How much email would be too much?" and the answer is always the same calm and reassuring response: "We can talk about it, if that happens".)