Am I to Blame?

Recently I have been experiencing problems in my marriage. For context this is my second marriage. We have only been married for 3 and a half years. My husband is 10 years younger than me. We lived together for 2 years before he proposed. Now that that's out of the way, my husband suffers from insomnia. It had gotten pretty bad to the point where we've taken him to the ER to be given something to get him to sleep in the past. I do not have insomnia. I work daytime 7-5. He currently works nights 4p to 1a. He does actually get sleep now during the day. We are both gamers and both had our consoles set up in the bedroom. Previously his routine was to come home and play his games/ chat with his friends in game until he became tired and could sleep. This would cause me to lose sleep since he played in our room. I tried to compromise by using ear plugs and sleep masks so I could sleep through the noise and bright light. For myself I need a dark and quiet room to sleep. He would usually sleep with the TV on claiming the background noise helped him. I find out that extended use of ear plugs was actually harming to my ears. He wound up moving his gaming stuff into the living room. I love and adore my husband. There were times when I felt snubbed because he would ignore me, preferring to play and chat with his online friends. I did mention this to him on several occasions and I will admit that I've come to resent his gaming buddies. He said I was the one that pushed him away. About 6 months ago he took a job working at Sonic. That's the 4 to 1 job he has right now. He sleeps during the day and wakes up around 2 or 3. He will remain in the living room when he comes home around 1 or 2 and won't come into the bedroom until around 5. I get up st 5 to get ready for work. So we basically don't actually sleep together. I'm an introvert. I don't think it's social society but I do feel drained after going shopping and doing errands. So on weekends when I do all the things like grocery shopping and errands I go alone in the mornings while he sleeps. By the time I get home I'm mentally exhausted. He would get up and ask if I wanted to here or there and I would decline. I'd explain to him I already went to the stores and was tired. He accused me of once again pushing him away. Not my intention at all and I did try explain this. He has made friends with his coworkers which is great. I found out recently he's been buying Starbucks, for his female coworkers. He's been giving a ride to and from work to a female coworker. She's also had him on call the last week on case she needed to go to the hospital/ER. I'll admit im a little salty about these things as it's triggered jealousy from me. He wasn't even there for me when I had to be at the hospital myself. Matter of fact here didn't even know. I did tell him, but it turns out it was a moment when he'd ignored me. I have tried to talk to him about it all but it always turns into an argument. He will go a month or more without having sex with me even. There's more details but this is getting pretty long winded and I'm sounding kinda lame.