Firstly want to offer my hugs - I threw my toys out the pram last night and believe every parent needs to find their support network as it is so tough! But you're doing it and your little girl is gaining weight so well done, you've done that, you're raising a little very demanding human - give yourself credit!
I also have a DD similar age (7weeks) and a DS (2 years) - likewise most of the childcare is down to me as DH works long hours. I'm BFing but DD is very refluxy and sicks up a lot so I do understand the nervousness of feeding in public (is some stranger going to get a lapful of milk as I hold her over my shoulder?!)
Firstly, do NOT feel bad about feeding in public - I'm sure she makes less mess than when she becomes a toddler who you feed when out!! What are you afraid other people are thinking? You're feeding your baby and doing your best to help her, sweetheart you're being her mother and caring for her - how can that possibly make you a bad mother?Get out and feed your DD in public and if she dribbles - she's a baby, count to 10 and relax - if YOU act relaxed about it so will everyone else.
Secondly, have you asked the doctor for anything to help with the thrush? Or asked for advice as to how long it'll last? If you know it'll clear in a couple of weeks then it's a focus as opposed to think 'ugh, she has this forever!!'
6 weeks for both my children has been a tripping point for me - you're out of the high of the newborn stage and sleep deprived - any issues that crop up at that point are bound to tip the scales. I noticed a huge change for the better once the 6 weeks passed as baby started finding a 'routine' of sorts and it all started becoming more normal.
Hang in there, things do get better and your confidence will soar, hope your DD's thrush clears soon