Fist off, don't beat yourself. The moms who have NEVER lost it with their los are the moms who have NEVER had a sleep issue. It is true, you do your best to be the best mom you can but as a pp said, we're only humans, therefore perfectibles. That meaning we are allowed to be angry, sad or desperated with the consequences those feelings bring along. Yes it is wrong to yell/shout/spank a little baby... but it is also wrong not to sleep so what else can you do? take a deep breath, pray to God for patience and give your best each day. If it gets twisted in the middle of it, well, there's always a tomorrow and as long as you love and nurture your lo, this "episodes" won't damage him for life.
Being that said, forget about the word SHAME. "I'm ashamed to ask for help to my SIL, she'll think I'm uncapable, MIL will talk about me for ages. I'm ashamed of not bringing a meal to that party... I'm ashamed that clothing is not ironed..." housework/duties can wait. Be sure to have nutricious meals in your fridge and avoid the house to be a war zone and that's it. If guest's bathroom is dirty... close it! and don't invite people to come over or just invite the closest ones and have them come to your own bathroom. Sleep training is a crisis period and should be dealt like it. Save your energy for it and not for pleasing people. Ask for all the help you think you can get, spend some savings in it (get a cleaner or pay one of your young cousins/nephews/siblings to babysit for a couple of hours). Spend at least 20 mins a day on YOU: do your hair or make up or a facial if you enjoy that. Tide up your drawers, look at pictures, read a book, paint your nails, do a craft. Just 20 mins a day to recharge your energy and strenght and confidence in yourself. It is soooo worth it even when there's piles of laundry and dishes waiting for you... who's gonna die if they're not done?
Vent and whine as much as you want/need/can. HEre, you will always find a listening ear and many brains to think of a solution.
I feel for you, been there and it is an AWFUL feeling. I hope it ends soon for you. Take care. Many hugs going your way!