You must be exhausted and sleep depravation is a condition that I think is not taken seriously enough.
My first child was like yours.
At this point you will be at your lowest, all of your reserve energy is gone and you are just running on empty.
I had to go back to work after 6 months to a high pressure job and after a month I was a total mess.
In desperation one night, I put on headphones and watched a film whilst he cried. I knew he was safe and well, but I still worried I had damaged him in some way. As the credits rolled the crying stopped. I crept into his room and he was asleep.
I was still worried about him, but in the morning he had a big smile on his face when he woke up and after that he slept through the night, unless he was ill.
He is now an adult and I still feel it was the hardest thing I have done, even though it only lasted a few hours.
Also, I found blackout blinds taped to the windows and blackout curtain linings to help in keeping my children sleep longer in the summer months.