OP - I have also had a premature baby (mine is still in hospital). It's a very worrying, traumatic experience - many of the mums I know from the hospital have post-traumatic stress disorder or have started taking antidepressants.
The worry also doesn't stop when you get home, as you lose the security of hospital staff/monitors so are often second guessing yourself or constantly checking baby.
I have felt like you. I managed for a while but the sheer exhaustion and feeling like I was letting everyone down made me feel that everyone would be better off if I wasn't here.
I went to the GP, who gave me the same a/ds as you. She said they were ok to take while expressing. They have taken the edge off things.
You are not alone in feeling how you do, but you will get through it.
Fwiw my little one also has reflux and it's really hard work - see if your GP will prescribe colief or gaviscon.
I actually felt lots better now I've given up expressing - I found it exhausting expressing 6+ times a day. To be expressing and caring for a baby is exhausting and stress you don't need at the moment, but obviously it's your choice. The GP may also be able to suggest a comfort formula you could try to help the reflux.
From what you've said, your OH has no concept of depression and how bad you feel. Personally I would discount his view on antidepressants because of this. You need to get well. Please make an emergency appt with your GP (for you and baby) ASAP.