Oh OP, I was in exactly your position 8 years ago - on the post natal ward with sepsis whilst my DH looked after the baby at home. Then it snowed and he couldn't even visit. I was admitted when DS was 5 days old and home again when he turned 10 days.
Firstly, I understand exactly how you are feeling - I basically sobbed for about 3 days. As the antibiotics kicked in I started to feel a bit better because I could sleep, but I was absolutely devastated not to be with my baby. I remember one of the drs coming to tell me that there hadn't been much change and I was to stay longer, I just cried and cried. The midwives told me they see it all the time and that it was completely normal.
I stayed in for 5 days, they let me go home when the infection level had dropped and my stats had improved. My blood pressure was very high and so was my pulse so once they had done a few readings where they were heading in the right direction everything else sort of went into place. It felt like an age waiting for that to happen but it did eventually.
Those few days were the most miserable I've ever been and I really had to take care of myself when I got home. I did get home though and everything was fine. Whilst I was in people kept saying that I should enjoy the break which only made me cry more.
You will start to feel less teary soon OP, make sure you tell the midwives how you are feeling as they will offer you support. I really feel for you because even now I remember just how horrible it was. But, when I got home it was like I hadn't really been away. I was scared it would affect my bond with DS but it didn't at all. At first whenever I found it hard I put it down to not being there for those days, but after I had DS2 and no hospital stay I realised that it made no difference at all - same new mum struggles (hindsight is a wonderful thing!).
I hope you manage to get home soon, OP. Let yourself cry and accept that you feel a bit crap, you're not doing anything wrong. It's healthy to accept it and that will help you to come to terms with what's happening. I wish I'd had mumsnet when I was going through this but I didn't know it existed!
Look after yourself and congratulations on your newborn. You'll be home before you know it.