Several things to tackle there.
The first (and I mean this gently) is that even in your writing I can feel how frantic you seem, this could be catastrophising and this is actually a symptom of your mental health. You gave birth 6 weeks ago, be kind to yourself.
Regarding Toddler:
You can teach your toddler to stay away from baby. It just needs firm boundaries and repetition. There was 14 months between my oldest two and even at that age she quickly learnt.
I had a yellow cot blanket that I kept on the floor. This was "baby space". Toddler was allowed to sit outside blanket and play with baby, but not get onto blanket. Every time she went onto the blanket is say no, lift her and put into travel cot just for 15 seconds or so. Enough time yo say "No, that is baby space". Then back out. Repeat every time she went on the blanket. She learnt quickly.
Now my method was for a very, very young toddler with very little language skills. An older toddler might need a different approach. But it meant that I could put bouncer, Moses basket, or pushchair on blanket and toddler understand to leave baby when on yellow blanket.
Regarding Swaddle
A baby screaming and agitated needs a swaddle more. The swaddle is there to calm and angry and agitated baby. A calm baby wouldn't need a swaddle. The screaming means baby need help to calm. The sensory deprivation of the swaddle, and recreating womb-like conditions is exactly the primal help baby needs.
Baby in same room as you and toddler
This is necessary for Safe Sleep. Baby absolutely needs to be sleeping in the same room you are, including during the day. It's a SIDS risk not to. Since toddler will also need to be with you, you simply have to find a way to make it work. Putting baby upstairs in the cot with you downstairs isn't something to do until after 6 months.