It's OK to say you've had enough of feeding for now and put her down or let someone else take her for a bit. On demand feeding does not mean at the expense of your own mental health. And yes if you want to give one bottle that's not going to be the end of breastfeeding - do what you need to do to be comfortable right now.
That said it sounds like there is probably more going on here than a growth spurt. Has your baby been competently assessed for tongue tie? I am thinking: nipple shield use sounds as though the latch may have been difficult/painful, potentially from the start? Recurrent mastitis suggests the breast is not being drained effectively, which in combination with frequent feeds suggests to me potential latch/milk transfer problems of some kind. (Not supply problems, though you may have had some sense that your supply could be low) "Various problems" hints this is a pattern which may have been there since birth.
Who have you seen for breastfeeding support so far? I am thinking this is probably beyond the experience of most health visitors, midwives and GPs unless you've been exceptionally lucky to find one who has extensive personal knowledge about breastfeeding. I would recommend (if you have not already) to move to the "next step" which to me is the free or low cost but breastfeeding-specific resources, that you may have to seek out yourself: the breastfeeding helplines (La Leche League's runs over the weekend but be aware it's in the helper's home so do state "I'm phoning for breastfeeding support" and wait to get confirmation you're speaking to the right person, don't just launch into a description of your breast to a person's poor husband as I once did
to his credit he was completely unruffled and just got his wife :o), any local breastfeeding support group (google breastfeeding support + town), NCT breastfeeding counsellors, La Leche League groups, Baby Cafes.
If you already know someone/something at this level go back to them. If you can't find anything locally or need to go one step further, search for a local IBCLC. Some run groups for a low cost but most are private practitioners who charge for their time. However it is worth a phone call or email, even if you think you can't afford to pay for help. Just see what they say.