You poor thing! I had an abscess in my left breast about 6 weeks ago and I'm still breastfeeding from both sides. It is pretty horrific while it's happening, but I'm healed apart from a couple of very small scars.
Getting diagnosed is a very important first step (mine was missed by 3! GPs) and you will start to feel better almost as soon as you start getting properly treated. The treatment itself isn't pleasant, but what needs doing varies very much on how large the abscess is, what stage it's diagnosed at, but I only needed to be treated over four days, and then it took about another 3 weeks for 'the hole' to fully heal.
Make sure you look after yourself and get as much rest as you can (easier said than done with 3 DCs :( ) you are properly ill if you have an abscess, and now would be the time to call in favours to help look after you and the kids.
I totally understand where you're coming from feeling let down by what is supposed to be a lovely experience. The antibiotics made DD grotty too, and I can remember being in agony and thinking that in trying to do the 'right' thing by BFing I was making both of us ill - an absolute low point for me. I don't know how old your DD is, but I focused on the fact that my DD had started to break off mid-feed to give me. Big milky grin. You could also lookfor the NCT reasons to be proud chart - it's on the Internet if you google it.
Everyone who treated me was very clear that you really need to keep feeding, even if after you've healed you decide you've had enough. a baby feeding is the best way of getting milk out of the breast. It is absolutely excruciating though - I squeezed DP's hand during feeds, harder than I did during labour!
Feel free to message me, or chat on here if you want to moan. One of the worst things is that it's so rare that very few people will know what you're going through!
In short, it is very unfair and to be honest pretty shitty, but you can keep feeding if you want to, and if you do you should be very, very proud of yourself - I am! And even if you decide enough is enough, you've dine the best that you can for your DD, and you should still be proud of yourself! Good luck, and very un-mumsnetty hugs!