Living, As a male I would suggest, regardless of his mental state, that your boyfriend accept the responsibility of organising transport for you. The last thing you need is the pressure of not seeing medical help. Having a child is a tremendous strain on a woman and she needs every bit of help the father has. Tell him you cannot deal with it and ask him to organise your attendances as required. Surely he has mates who have cars. He will know someone who can help, even a neighbour but let him carry the weight of that for you.
Try and take it easy on yourself, you are not responsible for everything that happens, it's just life.