Maybe if you answer the following, people will be able to help you better.
When did you land? Have you made any trips to Canada after that?
When is your due date?
To which province do you plan to move?
What are your countries of residence and citizenship?
Does your spouse (child's father) have PR also?
Some brief notes.
If the child is born in Canada, they are Canadian citizens and they will get provincial health coverage from day one (I am not 100% sure if immediate provincial health coverage is conditional on being born in Canada or whether the mother has provincial health coverage at the time of birth). However, if you yourself don't have provincial health coverage at that time, your delivery charges will not be covered.
You don't have to worry about child's medical exam too much. That is the least of your concerns.