Need Help-Constant fighting-am I the cause?

I've been married for 2.5 years and with my husband for about 4.5 years. We had a baby last December. Since having our daughter, I feel like our arguments have escalated in severity and frequency. We seem to argue about EVERYTHING. I just can't figure out why. Has anyone else experience more fighting when a child came along? I mean, our daughter is relatively easy, she sleeps well ,pretty even tempered so I don't think its exhaustion or sleep deprivation. A little background...I work full-time, my husband goes to school 2 days a week and watches our daughter the other days. Latest argument (and one of the most severe to date..at least in my husband POV): Yesterday I took the day off from work to take our daughter to her 9 month dr's appt. My husband had school until 3pm and then went to a personal training session at 4pm. He had told me that he had a REALLY bad day at school and it was obvious he was in a bad mood. He got home around 5pm and pretty much immediately went to the bedroom and laid down. Around 6pm, he woke up and my daughter and I went in to hang out with him. I was talking about an errand I needed to run and asked if he would go with me to which he said he did not feel like going anywhere, which was fine, next I said, ok then I'm going to leave our daughter with you so I can run my quick errand, and he said can't you take her with you. I said it will only be 30 minutes, and I just don't want to have to get her in and out of the car (me thinking that I'm perfectly willing to take care of her all night if he can just watch her for 30 minutes) and his response was "I was hoping for a little alone time". Well, this made me exceptionally angry because not only had he been gone all day and I had been with our daughter all day, but he had already gone to a training appt and also napped in the bedroom. The he got angry at me for getting angry with him and the whole thing spun into a HUGE argument where he absolutely refused to believe that I had a valid reason to get upset and it was all me. Fast forward to today and we are still not really speaking and we had a brief phone call where I tried to just say I'm sorry for fighting but he accused me of not being genuine in my apology and he still refuses to believe that I had any right to be angry. He says I am not empathetic because I couldn't see that he had just had a really bad day and I shouldn't have been unwilling to take our daughter (which I did end up taking her). I was being insensitive and uncaring. We have had several arguments over what he sees as my lack of affection toward him (which I will admit I do struggle with physical affection and saying I love you, a life long struggle) and he also accuses me of always thinking he is the bad guy in a situation. I on the other hand, think that we both play our parts in arguments and I am just as guilty sometimes, but in this case, I feel he is bringing other resentments into this argument and simply refuses to see my side. Am I wrong? Was I insensitive in this case? I just need to figure out if I truly am the root cause of our fighting.

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