Hugs @firsttimemum34. It's really overwhelming coping with a newborn.
It's normal to feel some anxiety I reckon, but you have to draw the line when it stops you from doing things you'd normally enjoy - like going for a coffee.
Make sure you tell these things to your GP so they can assess you accurately for PND.
Also are you getting out in the sun for a walk with bub? I know you're tired but honestly even 5-10 minutes will make you feel better.
And about the baby bath. My mum gave me this awesome sling chair that goes in the bath and bub reclines on it - makes the bathing process much easier as he's better supported. The brand is Infa-Secure.