I would have responded in the same way as you when my ds was tiny, but now I can see it is the post baby madness. I do think fathers should be kind about our insanity - eg not leave the baby near an open door when we have explained it makes us have heart failure - but I don't think we can expect them to realise in advance what is going to set us off - they truly have not got the same hormonal maelstrom and that fierce protective urge.
About the shouting - I think he is tired, emotional, trying to adjust to all the upheaval and responsibility of being a new father, and feeling attacked by you when he needs reassurance that he is being a good provider for you and the baby. I am not trying to take sides, just pointing out what men want at this stage. Dp and I had similar rows when ds was small (well if truth be told we still do sometimes, but I remember very clearly how intense it all felt then). It is not worth losing the father of your child over a bit of swearing and lost tempers. Nor over a possible misjudgement about safety (I personally can't see the prob with leaving the baby downstairs, but I was not there, and it is your baby not mine).
Do try to make it up to him - tell him you appreciate all that he does for you, what a great dad he is etc. Ask him to be extra kind to you right now as you are so vulnerable. Remind him it upsets you when he shouts and swears. However I think shouting and swearing is actually quite a good way to deal with anger - better than fists - so you may want to reconsider this one!
I don't know whether you are depressed or not - you sound just like me when I was a new mother - and I certainly wasn't depressed, just madly, insanely in love with my new baby. However if you think ADs will help then try them - no point not taking medication if it would help you. However these early months are never going to be a breeze, with or without ADs. Try to pull together and remember you are in this for the long haul. When your ds is 20 you won't care whether he was left downstairs with the door open for half an hour, but you will care that he had his father around for him and for you while he was growing into a young man.