First, welcome to the forums and I hope that you are doing OK in what are challenging times.
Dealing with family members, friends or loved ones who are going through depression and anxiety can be incredibly testing as you can sometimes feel like you are flying blind. However, from what I can see, you do seem to be supporting her which is a wonderful thing for you to be doing. Unfortunately, there is not a perfect fit on what works for each individual, but the fact that you have said that you are there for your sister is the biggest thing that you can do. Do you know if she has confided about her emotions with any other family members, friends or loved ones? I have included some resources below that might hopefully be of assistance in helping others.
You should take comfort in the fact that your sister does seem to me making the right moves by seeing someone else and not putting all the burden onto yourself. As much as we want to take away the pain, this can sometimes be a multi-step process. What is true though is that you are proving yourself to be an important step on her journey.
I am very sorry to heat that you are struggling with your mental health and are noticing that you are feeling emotionally and physically tired. When you are going through the challenge of supporting others, you should also make sure that you are carving out enough time to look after yourself too. This could be something as simple as some mindfulness exercises to make you feel more relaxed, or ensuring you are getting enough fresh air and light exercise to clear you head especially if you are having some challenging conversations in supporting your sister. It is important that you support yourself in this time also.
In case you aren't aware, there are some resources available besides these online forums if you ever need to chat to someone confidentially. This includes the online chat function that is available 3pm-Midnight daily AEST and the 24/7 Beyond Blue hotline 1300 224636. More detail below should you need it.
Of course, we are always here to help on the forums, so please write back with any questions you have or if something else comes up. I hope what I have said is useful to you.