Babies nurse almost 24/7 at that age. Literally my son spent day and night attached to my breast. I used to joke I "finished" netflix in the first 6 weeks of his life as I was stuck on the couch nursing him and watching netflix, lol.
Honestly, and this may sound blunt, if you want to continue breastfeeding you need to just let her do her thing. After the 3rd/4th week her feeds may space back out, and then at around 6 weeks, you will be in for it again. After that it is smooth sailing!
If you continue to feed from a bottle, especially formula, she will possibly refuse the breast and most likely you will loose supply.
Ductal thrush needs to be treated asap. It will not go away on it's own, and it can/will spread to your baby and cause her a lot of pain. It's a go to the doctor right now kind of situation. Also, once treated it will be gone in days, and after about 1.5/2 days you will feel about 80% better. If it isn't ductal thrush, you need to have her latch assessed. I've had ductal thrush. Twice. It hurt a lot, and pumping would have felt like madness on it, much worse than a baby breastfeeding. Which makes me think that it may be a latch issue. The other possibility for pain in the breast tissue is a blocked duct, and the best treatment for that is putting babe to the breast.
Having thrush and having a baby cluster feed is no indication that you can't breastfeed exclusively. Thrush is super common, especially if you had ab's during or after labour. It's painful, but also easily treated and usually doesn't return if medication is properly used. Cluster feeding is how a baby signals to your body to produce enough milk. If she isn't latched on, your body doesn't know to produce more.
I'm glad your baby is getting at least some breast milk, and you should be proud of that Momma. I just want to make sure you have all the information before you make any kind of decision that could harm your breastfeeding relationship. It is a whole lot easier to quit breastfeeding if you change your mind later on, than to try and reestablish breastfeeding after you have lost your milk and have a baby who has nipple confusion. Not that any of that will necessarily happen to you! If you have all the information and suggestions and you choose to combi feed or formula feed, that is your choice too! But I don't want you to believe you can't breastfeed because of a bout of thrush or because babe nurses frequently, because you totally can. I did it, made it through 2 bouts of ductal thrush, 2 bouts of mastitis, blocked ducts and a baby who would nurse for hours straight without stopping. Mommas are brilliant and resilient. Now at 8 months old I'm glad I breastfeed my son- no bottles to clean and sterilize or formula to mix, always available, anywhere, anytime at the perfect temperature with no sterilization required.
If you'd like some support about how to manage with thrush and a frequent nurser I'd be happy to help if you PM me!