First of all, kudos to you. Motherhood is indeed a huge adjustment and challenge. This has nothing to do with the fact that you truly love your children. Of course you do. Being responsible for them 24/7, however, 365 days a week, can be physical, emotionally and mentally very, very exhausting. Right at this very moment, I have my 3-year old crouched on my lap with a pen that I am trying to convince her to use on paper and not on my clothing or on her or my skin. Her older sister is sitting in the living room with a new dragon toy we bought today. She's into dragons. This is about the first quiet (yeah, right!) moment I have had all day. It won't last but a minute, I am sure. Dinner is cooking in the oven. The race continues constantly. I am surprised it is not a requirement that moms have therapeutic or psychological support in place the DAY they become pregnant.
So, on to your question -- a psychologist and a therapist are trained in often the same things, with the real difference being that a psychologist will often understand further the psychobiological changes that depression and anxiety can bring, whereas a therapist often has training in the result, but not so much the cause. Some do. Some do not. Degree-wise, a therapist will usually have an LPC, MSW, LCSW or MFT degree. A psychologist will have a Psy.D or a Ph.D. Both are doctors, whereas a therapist is often a master's level professional.
In my opinion, both are valuable. If you end up being prescribed an antidepressant, it might be useful for you to see a psychologist. He/She can help in explaining what biologically might be going on with you. If you've got the insurance coverage, see if you can have both.
I wish you all the love and support in the world.
All my best!