I agree with the others. Breastfeeding is tough the first couple of months (though steadily gets better so don't panic!) and when I had DD, my 2nd, I realised that you just have to give in to the breastfeeding and ignore everything else. Makes life a lot easier. With DS I tried to be superwoman... and failed.
I think you just need to get some practical help with things. First, the wrapping presents ... take them with you unwrapped along with a roll of paper. Ask someone else to wrap them when you get there. i.e. if it's your parents then ask your dad to wrap your mums and vice versa. Or stick everything in gift bags!
Can you write while you're feeding? If so, do a list of what you need to pack and then run round in a 10 min dash before you go. Or get your DH to rush round.
For the house, if it's really important to you, pick up any dirty washing and stick it in a cupboard. Put all rubbish in a bin bag. Pile everything else up. Apologise to your neighbour if you feel it's necessary. And you never know... she might clean the place lol.
DON'T beat yourself up for not managing a screaming 3 wk old and a house and Christmas. A screaming 3 wk old is more than enough for most people. Oh, and if a dummy works for you, no harm (both mine have).
If your baby naps at all, nap with him. Being slightly refreshed is far better than a clean house or wrapped pressies in the long run.
Stick with it as it is sooooo worth it. It's near impossible to see that in the first month or two, but it really is. I fed DS until a year and was gutted when we stopped even though I boiled the kettle for formula a couple of times a day for the first couple of and really couldn't see any light at the end of the tunnel. But it's lovely after that!