4 months is a big growth spurt time for babies, and does really interfere with their sleep. I feel for you and know exactly how you are feeling. DD was exactly the same.
Have a quick check to see if she has any teeth coming through and go see your Doctor as your DD may have silent reflux.
For naps, I'd just let her snooze away on my chest or in my arms and you get a nap too (this does make a huge difference to how you feel).
I BF until she feel asleep and then popped her in her basket. When she first woke for a feed I brought her into bed and she slept much better, and so did I.
Have you tried raising up the head of the cot (some books/bricks under the legs). Then making a sausage of a sheet and putting it in a U shape with your DD's bottom resting on it. This can help with reflux, or if she's just not comfy flat on her back.
Leave the housework and laundry. Eat quick and easy meals. Just preserve as much energy as you can, and eat as much as you can early in the day to keep up your milk yield.
Do you get out at all to any groups at all? I found that my local breastfeeding group at the surestart centre was great. You will see you are not alone and gain a huge amount of support.
Have you tried keeping your DD upright after feeding her? If she is suffering from reflux this will really help if you can do it for at least half an hour to keep the acid in her stomach. And try rubbing her back gently in an upwards motion.
It does feel like your whole world is collapsing around you, and it may not feel like it right now, but one day soon this will be a distant memory.
I have not done any "sleep training" with DD and she finally worked it all out and is now a great night sleeper but still crap at napping at 14 months.