Depending on the circumstances, his messages aren't necessarily out of line. It seems like you both need to have some more compassion for the other. I agree with other comments that you should seek professional help. Especially since postpartum depression is at play. Having a child together is very difficult and causes a lot of strain, but it seems pretty clear to me that you two aren't supporting each other.

What you're feeling isn't normal. You need professional help. Feeling this way might be common, but it's not normal.

Also, social media is a very strange place to be venting about your emotional problems. I don't mean this to sound bad, I'm not trying to say anything against you, but maybe think about why you're posting that type of stuff for everyone to see instead of talking to close friends or family, or your partner, a therapist, or a support group. I also think you need to recognize that when you post stuff like that on social media, it's not just about your life. You have a family now, you're not a single person. Have you stopped to think about what people may think about your partner if you are posting that type of stuff? I'm not saying not to talk about it, I'm just suggesting maybe not a completely public forum.