I'm very happy that your T is caring and offering support when you need it. As other said she would not offer something she is not willing to give.
In my case sometimes less means more. My first T never told me how she stands with between session contact so when I got overwhelmed once and send her email I did not know what she will tell me and that felt horrible as I hate to be told off. But she replied and said sending mails is ok. So I did send probably one email a month and she always replied. Problem was she told me one time I send more emails then other clients and that I have needs to be accepted more often then others. I felt horrible and very guilty. So even I was allowed emails and she replied it was very guilt provoking.
My current T allows emails too which she stated during first session but she doesn't reply as a rule unless it is an emergency. I send probably same amount of emails as before which is one a month but she never said it is too much. She even encourages me to write more. Last session she even hinted something about her replying to my email. I feel so much better about emailing with this T.