Oh god, firstly, you have my deepest sympathies. I have been there. It is horrible, you are not going crazy, little one's who don't sleep are THE HARDEST work on earth IMO.
Secondly, tell yourself that this isn't going to last forever, because it won't. I can't tell you when, but it will, 2 months, 3 months....could be next week, could be next year. I know it feels like it will never end, but it will....I was in exactly your place 2 years ago....and have come out the other side.
Have you tried light music or white noise, bbc news radio even? I agree with previous poster regarding a solid routine. I also found that sometimes light massage (squeezing) of baby's legs would settle him a bit, enough to drop off to sleep. We also had concerns about reflux, lactose issues and resorted to using Colief with his feeds. It did help a bit I think. Also, if it is a tummy issue, speak to GP and find out if they'd be okay with you giving LO some fenugreek tea once a day or so. It settles upset tummies and helps with gas etc...can't hurt.
Singing also helped, he seemed to really be into listening to me singing, funnily enough is brilliant singer now (for a toddler)....I digress
Bottom line, you will not go mad, you and your DP will be okay. One thing we did to cope was to each have every other night 'off' from baby...One night I waould deal with him while DP got some sleep in a quiet place in the house, the next he'd do it and I'd get a solid nights sleep. This really helped us a lot as a bit of rest really gives you the strength to deal with this sleepless mess the next day.
Big hug to you...it's so hard x