Hello Eagleray.
It sounds as though you are doing tremendously well. As the others have said, these are early days.
It sounds as though there have been a few things going on which have not helped the situation;
- being told to feed every 4 hrs
- possibly an inaccurate birthweight?
I agree with the others - just feed, feed, feed and feed some more. Forget the 4-hour thing. Babies love suckling, - for feeding and just as a general hobby I think! I don't think it would be too tiring for your DD?, esp not after 3 weeks of giving it a go. If nothing else, her being near you will be good for all the hormones to kick in to help milk production. I know you said that 3h feeds were tough going, so perhaps being advised to feed ++++ is not what you want to hear? In the long run, it will get your supply really well boosted and you'll be off FF before you know it.
Regarding expressing, I find that my supply is at its very best in the morning. If I need to express, I do it after DS's first "proper" feed of the day (as opposed to night). I wouldn't give FF in the morning at all, or any EBM. If you need to give her a bit, late afternoon/ early evening, just when you are maybe flagging a bit, is perhaps the better time to take the pressure of you, build your supplies.
From my sums, you gave your DD ~300ml of formula? I know it sounds like a heck of a lot of milk for you to just "produce" all of a sudden if you were to cut out the FF. However, I would have confidence in yourself to bridge the gap. Also, I think that the amount that a BF baby will take out a bottle is unreal. My DS is quite a sucky wee boy I think. I went out one night with my husband and his folks looked after him. I had a lot of EBM in the freezer and has fed DS before going out. In the course of 3h, he had been given 380ml. I kid you not. I nearly cried (having anticipated the supplies I had built up lasting a little longer...). I reckon though that he just enjoys sucking, and so every time he sucked a bottle dry, Granny got him another one. [not complaining - got a night out]. My point is....your DD has got good at sucking after 3 weeks and the amount she takes out a bottle might be more than she would be happy with if you were BF her.
The birthweight thing sounds like a lot of pressure on you [pressure and stress not good for supply]. I have some experience of this.
My DS was born at 34weeks, weighing 2.6kg. He was tube fed for about a week (FF and EBM), and I expressed, trying to feed him myself with the tube hanging out his mouth (latch pretty woeful as you'd imagine). Anyhow, he did get to grips with BF with time. However, he did lose probably >10% of his birthweight. When I got him home, by that time he was EBF, and the HV was pretty scary about his weight and that he was on about the 2nd centile("oh no, big boy, that's not good enough", type comments after weighing him). I was genuinely not concerned at all about his rate of growth - at the end of the day, the 2nd centile is still normal. He was happy. He was making wet and dirty nappies. He was feeding away.
HV and MW are well meaning, but alarmist types, sometimes I think. I really had to reassure them that I was very happy with his progress and that I didn't have concerns. I think they backed off because they knew I was a doctor, so didn't pressure me to supplement with FF or question me (too) much. But, I did feel I had to stick up for myself, and my wee boy and the plan for him to be EBF.
Getting up to express in the middle of the night when DS was in hospital was a PITA, sterilising things, freezing milk, etc etc. I can only imagine that making up FF is a massive PITA too, compared to the relative ease of just popping a baby on the boob. Hats off to you for persevering. Getting some personal advice is hopefully going to be helpful, but I would just like to encourage you, and I do really believe that when you have confidence in yourself to BF your baby, this will help you relax, help milk to come in, and stop you from asking yourself the awful is-my-baby-getting-enough question.
(Incidentally, even though I didn't every really have issues with my supply - I had to be expressing >750ml/24h before they'd let me take DS home..., if I wasn't eating well, or trying to do housework, or basically not looking after myself, or too tired, I found my supply wasn't so good. You sometimes really do need to put yourself first!).
Prob far too long and waffly. Hope if helps a bit though.