you say you don't want to appear needy - but lets be honest, by calling her multiple times during the week is being needy.
She is paid to see you for the hour, if you need more time, make an appointment to see her more often. T's need to have defined boundaries - maybe your last T went above and beyond but that was his boundaries, everyone is different.
And did you really need to call her? it obviously wasn't life or death as you are still here.
I think your T may interpret your calls in the first week of seeing her as you testing your boundaries.

I think maybe your T should have discussed with you things about calling/emailing out of session so that you knew what her response would be, instead of leaving you up to read her mind and interpret her non-response

You obviously had a great relationship with your previous T and must have been devastated by the sudden departure. Change of any kind is hard. You will be tempted to compare her every move to what your previous T would have done. Try not to be too harsh and give her some time to get to know you. If after a while you don't click, you can always change.