DS had silent reflux and barely slept, it was a horrendous time when DH went back, and I know how hard it can get.
My biggest tips are firstly, just remember that you're doing a great job, and forget all the 'shoulds' - like feeling that you 'should' have a clean house, dd 'should' sleep like all the perfect babies in books, or that you 'should' be presentable at any point of the day. As pps said, do whatever it takes to relax and rest, whether that is eating cereal for lunch (or dinner), watching lots of crap TV or napping at very odd times. For us a sling was our most important piece of baby kit - it kept the reflux at bay, the baby asleep or at least calm, and I had hands free.
Secondly, you sound like you could do with more support. Do you have someone who could come over and hold the baby for a little bit while you shower/nap/eat/cry? Or at least make you some food and a cup of tea or do some hoovering while you hold the baby? Also, DH needs to be aware that caring for a small baby is also a full time job, so if he is not taking any role in the evenings then he is working 8 hours a day while you work 24. My DH is not the most hands on dad, but even he took the baby in the sling for a few hours sleep at nights (often he'd do 9 till midnight, ideally while DS slept but if not then he would rock, shush etc and only bring into me for urgent feeds). Lots of other partners do late nights too. It may sound tricky for your DH, but ultimately it's a lot less tricky than if you end up exhausted to the point of collapse or PND, when he'd have to take over a lot more.
Is your dd on medication? It hasn't been a silver bullet for DS but meds and/or dairy and soy elimination (for at least a week) has been very helpful for lots of silent reflux babies on these forums.
Finally, I bf and think it does get easier and easier and is totally worth it, BUT if you are beyond it and need a rest, don't feel at all guilty about a dummy or some ff, your child needs a well mother more than it needs breast milk.
It does get so much easier - people kept telling me this and it felt like such a long way away, but in no time at all you'll have a 4 month old and chatting to friends about how yeah, the first few weeks were a bit tricky but you got through!