I sympathise. I have experienced this type of sleep deprivation a few nights in a row (due to wind - not overfeeding) and it is the worst kind of torture. It leaves you feeling teary & desperate. I also know that frequent feeding leaves your nipples terribly sore. You must be having a difficult time, especially with a 2 year old to deal with also. Just know that you are not alone & it won't last forever!
Similarly, my little one is only 2 1/2 weeks and constantly looking to suck on her hands. Because she's so unco-ordinated she can't seem to get them to her mouth before she chucks a wobbly. I'm guessing your little man might look to the breast for comfort in a similar way. I have found a dummy to be a great help during these times. The widwife that visited me at home actually suggested it. When breastfeeding get a nice big cherry dummy (Happy Baby are good - and cheap) one to fill their mouth so it doesn't cause them to clamp down on your nipple when they do feed. It might take him a little bit to get used to.
Also, I can only suggest giving your bub a bottle of formula last feed at night. I have done this three times now when my boobs are killing me and bub seems hungry. It gets you about 5 hrs sleep which I think we can all agree is heaven.