Is having my newborn tearing apart my relationship?

I just had my daughter last Friday & already feel some tension in my relationship... 
my fiancé seems distant and not very interested in our daughter. He was a big help the first couple days then just kind of started being a little distant. He hasn't kissed me or hugged me or told me he loved me without me trying first... I'm a pretty frail person when it comes to my relationship. My love language is physical touch and he knows this... but when I was pregnant we also didn't have sex since September and obviously can't for a couple more weeks... but even then idk if he will want to. Idk if he is a little weirded out by watching me give birth or what...
Also, he like ONLY shows my 3 yo stepdaughter attention. She is a lot more clingy right now bc of the baby and I understand that, but I feel like he isn't balancing them both well... I haven't had a chance to talk to him as family has been around almost constantly. We stayed at my parents house last night bc him and my dad had to go an hour out of town to take care of some other family business... & I don't want to have the conversation here or with my step daughter around, bc it's really hard to talk with her around. 
He left this morning only saying bye to her and asking for cuddles from her but didn't even hug me bye or give our newborn daughter a kiss... he just said, "Will you watch her (3yo) around the dogs?" & of course I always do... and said yes. Idk if it's too soon for me to ask him why isn't he showing our newborn more attention or if I'm being silly, but like I said... I am pretty sensitive when it comes to love with him. 
Also, yesterday he got pissed at me bc I had to have a talk with the neighbor under us bc she's banged on her ceiling bc our 3yo walks heavy and we have wood floors on the 2nd floor they only put in for us bc of my stepdaughters allergies, so our apartment isn't very sound proof. She called the office on us instead of just  trying to have a talk with us. She also had a 3 or 4 yo I noticed when I went to speak with her and the conversation got a little heated to say the least. Anyway, when I came back upstairs I was obviously frustrated by the situation and explained what happened to my fiancé... we proceeded to get ready, packing to stay at my parents and our 3yo was going back and forth walking heavily again and since I just spoke with the woman, I wanted her to sit down until it was time to go.. well she tried to run away from me and not listen when I told her to sit down so I picked her up and put her on the bed. Mind you, I have never whooped her or disciplined her physically... she starts crying and saying her arm is broke and just went dramatic on me and my fiancé is frustrated with me instead of asking what's going on and why isn't she listening when I say to do something... all while I'm trying to get everyone's shit together including EVERYTHING I need for a newborn! 
I was clearly more frustrated then and just felt like breaking down.. he then says, "what's your problem?" I tell him I'm frustrated bc of the neighbor, getting shit together and 3yo not listening... and he tells me "Well you don't have to take it out on us (him and 3yo)!" And knocks a pillow of the bed.. 
You know I am very stressed.. like idk what's going on with us and a newborn requires all my attention and I just feel like he doesn't understand how physically and emotionally exhausted I am. I love my baby and my family but I feel like it's him and his daughter against me and our newborn. That's what it feels like...