I lost my beloved dog Cody on the 11th. I am on anti depressents as well but they definitely are not stopping me from feeling the grief. I had a lot of anticipatory grief as we found out he had a large brain tumor in November so I have been crying on and off knowing what was to come. I think what you are experiencing may have something to do with the Paxil but without it would you have gone off the deep end? I probably would of if I wasn't on my medication. Maybe the fact that you aren't around where your baby lived is lessening your grief as well because your dog was living with your parents. I've noticed that when I'm not around my house or doing things I used to do with him I'm OK but at home, especially at night when we used to go for our nightly walks, give snacks, watch TV together and mostly when I go to bed because he used to sleep with me, I am a mess. Just my opinion. I think given the circumstances you are processing it "normally" (whatever that is). Take care of yourself everyone processes differently.
"Grief only exists where love lived first."--Franchesca Cox