some problems are unresolvable, but it sounds to me like yours may not be one of them. It does sounds like an attachment problem, perhaps as a result of your flat nipple which will make it harder for your bub to latch on properly and drain the breast (hence the mastitis). You have a few options.

You can continue expressing from the painful side, which for some women is a long term option although obviously it is not as easy as feeding straight from the breast.

You could try drawing the nipple out before a feed with ice and see if that helps bub attach. Also try the football hold incase bub doesn't like attaching from the right, some babies have a preferred side to lie on when they feed.

You could feed long term from only the right breast. You will be able to make enough milk from just one breast, although initially would have to work to build up the supply by offering more frequent feeds.

For now I would suggest resting the left side from feeding (but not expressing as it will keep your milk up whilst you make a decision) and give yourself a break from the pain, then speak to your MCHN or go to an ABA meeting where a LC will be able to watch your attachment without you having to pay for a private consultation.