He sounds like he could be on the autism spectrum. I would suggest a visit to a GP, work out a 'care plan' so you can have Medicare subsidised visits to a child psychologist. From there they can organise any testing or referrals.
Your child might be different but there is nothing wrong with that. The world would be boring if there were no quirks.
Love him for him and love him the way he is. He's your child and he's amazing.
Best of luck mate.

Talk to your GP and ask for a referral to speech therapist to help with speech (him having a hard time communicating could be a big cause of some of his frustration and tantrums) and pediatrician to get him checked out. If there is something he needs help with , getting help early is so important for him and you, to help everyone cope and function better. Kids who receive early intervention have much better outcomes than those who have issues caught later. If he watches a lot of T.V, cut back gradually until you only use it for when you really need a break. Too much tv can delay language development and cause behaviour issues. Read the book 1,2,3 magic- it works even for kids with special needs. Get him into daycare or preschool (if he’s not already) so you can have a break and also so he’s already in the routine of going before new Bub comes and doesn’t associate it with being shipped off because new baby is there. The educators will also be able to give you an idea of where he is at developmentally and pick up any red flags. I’m an Early Childhood teacher and I don’t want to upset you, but the things that you’ve mentioned about his speech at almost 3 are sending up a red flag for me. Take him to see GP or family health nurse ASAP- wait lists to see peadiatricians through the public health system are long, so get a referral ASAP. Good luck xox

Don’t be scared all toddlers are different!
I think maybe try more structure and routine, if he isn’t in daycare I recommend putting him into it at least twice a week!
If you can and you are desperate try changing is diet to gluten free and cut out a lot of sugar!

Go to your doctor, you need serious help.... having a 2 yr old up till 4/5 is totally unacceptable and will contributing to his behaviour issues during the day (and his speech development) .... GET PROFESSIONAL HELP BEFORE YOU HAVE THE BABY..... Things must be so hard for you..... It will get better xxx

Sounds like you need structure for one ie sleeping pattern. In regards to speech I would suggest talking to your doctor and as for the screaming his just trying to get his own way time out is a good thing.