My second daughter had bad reflux – it's HARD! Many people find the newborn stage very hard and unrewarding without reflux in the picture, and you've not only got that, but you're coming off of a very difficult pregnancy. Right now, getting you and your daughter through each day and night is an achievement. Please try not to draw any conclusions about whether you're cut out for motherhood or not based on this extremely difficult period.
Now, back to the reflux... Firstly, is she in pain with it? If so, the medication needs adjusting. How recently was she weighed to adjust the omeprazole dose? They can gain really quickly at this age. You may need to be seen by a paediatrician or feeding specialist if they need to increase the omeprazole dose per kg (rather than just upping the amount because she's bigger), but there is usually scope to adjust this if needed. I'm not sure how much adjustability there is with gaviscon. Carobel I know you can adjust some to try and reduce the amount they are sick. (My daughter didn't get on with either of them, though, so we only did a very brief trial of each thickener.) She was breastfed, though – bottle fed is easier for carobel/gaviscon.
For the actual being sick, does being upright help her? If so, have you got a sling that's comfortable for you and her so you and your partner can wear her as much as possible? What sort of bouncer have you got? A babybjorn or similar with adjustable angles can be good if she needs to be a bit more upright, plus the whole cover pulls off and goes in the washing machine. You can get spare covers for whilst it's washing/drying. We didn't but I did find myself ironing the cover dry a couple times.
For nappy changes and dressing, try rolling her to the side rather than lifting her legs. Lifting her legs used to just squeeze the milk out of my daughter. Also put a muslin/flannel/whatever under her head or on her chest or both, wherever she is usually sick (under the head for us, and it saved many hair washes).
We just didn't have our daughter on the better/less washable furniture for a good few months, but you also need good protective layers (harder if she projectile vomits, though). I like the Little Green Sheep mattress protectors – they don't rustle and the fabric coating is comfortable enough to lie on directly, so baby can lie on that on the floor/in the play gym/hanging out with you on the sofa. (We do also use them as intended, as a protective layer under sheets on the bed) Some of the travel changing mats are comfortable enough and hard wearing enough to use the same way, especially those from reusable nappy brands.
Sorry, that's a huge essay, but I hope there's something there that's helpful. Most of all though, it's not just you, this is really hard to deal with – but it will get better. One day you will realise the pile of milky washing is a bit smaller or that only baby had an outfit change today due to sick, not you or that they sat up on your lap for more than 10 seconds without being sick. And then gradually it will fade out of both of your lives.