I've read the numerous other threads you've started on this over the last couple of days.
Imo the issue is your anxiety. Give your setraline time to work. When are you next due to see your GP? Maybe book an earlier appointment and tell them what you've written here.
It is anxiety inducing having a DC (your first / only?) start nursery. Even more do this cohort that lacked socialisation due to lockdowns.
Has she been to any playgroups before?
Does DD want to go to nursery?
Ask for a meeting with the nursery manager and tell them about your anxiety and that the comments before about the blood have made you more anxious.
A couple of incidents of hitting during the settling in period is entirely normal.
The best place to tackle behaviour issues is in nursery.
Also your anxiety will lesson when you get time out from DD. Use this time to relax.
Where is her father in this? What does he think? Is he around? Can he speak to the nursery? Do the pick ups?
You do sound like you need more support.
I would definitely caution against removing her. Not only for her and your benefit but it will ring safeguarding alarm bells on top of the picture of blood (they will suspect domestic abuse) and your mental health difficulties. It will look like you are trying to hide her from services.
Contact your health visitor and ask for a visit to discuss all of this. They are best placed to advise you.