I'm so sorry you're going through this that sounds heartbreaking. I have a 2 year old who I co-sleep with. I spent one night away from him to give birth to my daughter and in the weeks after that he was exactly the same as your son. He would wake up screaming in the night bawling his eyes out upset thinking I wasn't there, even though I was right next to him. This was 3 months ago and even now, every time he wakes up, he screams before he even fully awake. As soon as he realises I'm there, he goes back to sleep.
Can your son talk yet at all? If he can you could try saying to him mamas here, or I'm here, give him a cuddle to reassure him you're there and lay in bed with him until he falls asleep, then leave. This is what I do with my son when he naps. I stay in bed with him until he's asleep, then I leave. At first he would wake up extremely upset, but after a few weeks he stopped getting upset. Now he just gets up out of bed from his nap and comes to find me in the living room.
Persistence is key with this one. I would personally absolutely not ignore him, as he is still very young and needs to know you are there. He needs the physical and emotional reassurance. Once he learns you are there, and even when you're not there when he wakes up but you are still in the building just in another room, I am sure he will be okay.
Takeaway point from this lengthy (sorry) reply - get him to nap/bed with you lay next to him, when he wakes up upset, attend to him immediately so he has the reassuranc of knowing you're there, stay with him while he falls asleep, then leave. If he wakes up upset again, go back in and do it again, get him back to sleep and leave. Be very persistent with this, it will take time but it is a learning process, in the end he will learn you are still there even though he can't see/feel you. This is what worked for me.
Good luck, hope this helps!