Your ex is a cretin for what he did to you. Chucking you out like that with no warning and no time to get your things together. What a bastard! Unless there was some "in extremis" back story/situation that we're not privy to (like: he's just found you in bed with another guy), then you've got nothing to be ashamed or embarrassed about, he does!! Don't blame yourself for any of it!
First off, you can get through this without him. He's shown you who he is and how easily he'd bail (I can't even get my head around that...no talking through things etc, just straight to dumping, bloody hell). You don't want that crap around you and your son.
Give yourself some time to get things straight in your head. Your life has been turned on its head in less than 24hrs. Let your friends and family know what has happened so that they can support you. My son's dad dumped me at a similar time when I was pregnant (I was 25yrs old and we'd been together 3yrs). There was an OW. I was heartbroken and a bloody mess. Don't do what I did and beg him to talk/come back/see things your way/try and sort things out. My ex and OW just turned nasty, which made things worse. His family were really close to me and were furious with him (I was lucky, they were amazing). I got practical stuff sorted, and told friends/family who were amazing. I managed to find a flat to rent and I knew job/Mat Pay would be ok. A lot of the furniture and bits I got were second hand or passed on to me.
Ex didn't go on birth certificate as we weren't married and he didn't come with me when I registered the birth. I'd not have your ex on birth certificate if I were you (i.e. register the birth without him!). Him being on birth cert will give him automatic PR (same rights as you). He can veto school choices, travel, all sorts...he can also refuse to return your DS if he was to have him for a couple of hours. You can still get child maintenance without him being on the birth cert (unless things have changed in past 18yrs!!). Check what things you're entitled to (child benefit, UC etc) and how/when to apply.
My ex eventually got in contact with me when DS was about 3. He sorted his shit out, apologised profusely to me (and our families!) and started to take a proper and active role in DS's life. After a good few years of him proving himself as a decent co-parent, and being respectful towards me, I arranged for him to be put on the birth certificate (it was easy enough for me to arrange at the registry office). But don't bank on this sort of thing happening.
If you need furniture etc, have a nosey on the freecycle sites and on FB market. You can pick up some fab stuff on there. Keep things simple for time being. Get on to housing/council/HA to register, and see if there is anything available/what wait times are - or if they can signpost you to secure rentals. Have you got much baby stuff? Again, keep that simple - babies aren't interested in lots of pricey things. Let your midwife know what's happened so they can support you. Please don't be scared, you'll do alright. I'm nearly 19yrs on from where you are now, and things are great - I have two beautiful kids, a good career, and life is good. x