It sounds like you are a wonderful and caring mother, your little girl is lucky to have you as her mum. I remember the first few months with my dd1 were so hard. I would be crying by breakfast time some days, from sheer exhaustion and worrying about poor feeding etc. I felt completely overwhelmed, it is such a hugely life changing event having your first child it takes some time to adapt and to feel confident in caring for your baby.
I remember feeling very isolated, like you my family are in a different country so at the time my only contacts were in a mother and baby group and as my baby had a few issues with feeding and slow growth I felt more anxious going to the group and seeing what she should have been doing that I stopped attending. I did a lot of walking with dd1 and am trying to do it now too as it does make me feel better mentally if I get out of the house plus it's good exercise.
It's a scary feeling being totally responsible for another human being. The first three months are the hardest, then as the baby establishes some kind of routine it does gradually start to get easier.
My dd3 is now 14 wks and only now are we starting to sleep until 5 am some nights and it is killing me! The weight will come off too, 9 wks is still very early to be back to your pre pregnancy size, you will get there, it just takes time. After 9 months of pregnancy though I do understand how you just want your old body back though and to feel in some way normal again.
If you are formula feeding/expressing perhaps your dh could give you a couple of nights off at the weekend and feed the baby so you can rest. Do talk to your doctor about how you feel. You are not a failure, you have a happy healthy baby and that is down to your love and care.