First, since you are not married you will have to name him as the father for his name to be on the birth certificate. I do not suggest that you avoid putting his name on there to keep him from having any type of custody though because that will really only cause problems later. Since you know that he is the father, your best scenario is to leave if you are planning to, have the child and then work on some sort of shared custody. This way you will also be able to get support for your unborn child. A judge rarely takes a newborn away from the mother completely unless she is unable to care for the child. That does not mean that the father does not have rights to custody and visitation, but you do not have to consent to him having primary custody.
My suggestion is that you do not decide anything while you are angry. If you are planning to move, then you should do so based on what is best for you and your children.
Until custody is decided in court, both parents have an equal right to the child. You and your boyfriend are the parents. The fact that you are not married does not change that fact.
I’m not certain about the 2 days, but I believe that you legally would have more time than that to find another place to live if you have been paying any of the current living expenses.