It took my first baby 8 weeks to get it, and even then she could only work the right side. It was another 2 weeks before she got the other side. I get your pain - I was trying to bf, then cup feeding, then expressing, then getting about 40 mins off before starting it all again.
I’d read that there are actually very few women that medically cannot breast feed. It is possible that you are one that cannot, but statistically I’d rule out other technique related factors IF you are keen to breast feed.
Get her latch checked and double check for tongue ties first of all. Can she latch - I have quite big boobs and it took me weeks to work out I needed to hold the baby in one arm and use my opposite hand to hold my breast in place, rather than trying to move the baby. There are loads of positions to try - lying down is also sometimes better.
Assuming all is well there, look at stimulating production.
Milk production is based on supply and demand. Your baby is sucking to get your supply up and running - if you give up and give a bottle then she will not be stimulating you enough so supply reduces, so you give another bottle and the cycle continues. You need to let her keep cluster feeding I’m afraid. It is painful at first, but not forever. Keep using the nipple cream to sooth. After a few weeks you won’t feel it at all.
There are foods to increase milk production - oats etc... Try google for these and other tips. Also, it’s so important to keep hydrated.
Being in the right frame of mind helps too. Milk release is affected by hormones do you need to try to relax, thing if your baby and / or listen to baby sounds, crying etc....
Sit on the sofa with a drink, hob nobs, the tv remote and a book - relax as much as possible, get comfy and just let her latch as and when she wants.
BF is a skill which can be hard, but to mention painful, to master. No one seems to tell you this, which is why I think so many get disheartened and give up. But, if you persevere and crack it, I personally found it so much easier for so many reasons (cost, convenience, lack of constant sterilising - brought of that with 8 weeks of cleaning pump bits). Both of you need to learn and you DD will get better as she works it out and with practice.
Pumping is strange IME. Oddly enough, with my second she “got it” immediately but I’ve been unable to pump much at all. She’s getting enough from source though (10 lbs plus at birth and gained weight fine). With my first I pumped gallons (same brand of pump and everything). Doesn’t make logical sense.
If you are keen to BF I hope the above helps. However, if it’s too stressful, painful or difficult, or you just don’t want to continue then don’t. It was the worst bit out of everything for me (including drug free birth and stitches) but I loved it once the initial learning period was over. But I never bottle fed so I have nothing to compare it to.
The best advice I ever got was that it’s not worth getting upset over. Try if you want to and if it doesn’t work out, just bottle feed. Baby’s react to their mummy’s stress do they’d rather you were happy, even if it means a bottle. There are millions of bottle fed babies out there and it is nothing to be ashamed of.
That was quite long, but I hope it helps. Good luck.