Need advice 40+2 PLEASE READ

I’m about to be past my due date by 3 days and I haven’t been to the doctor since 37 weeks.. I tried calling to schedule an appointment but they don’t have an availability until the middle of January and I would be past 43 weeks.. I tried to call the hospital I’m gonna have him at to ask what I should do but they didn’t answer.. I have no idea what to do and baby doesn’t seem like he’s coming any time soon.. do I just wait it out for him to come?

Update: Thank you for those who commented. I actually received a call from my doctors office asking if I’ve had the baby yet and I told them I hadn’t been seen since 37 weeks and explained to them that I tried calling to make an appointment but there wasn’t an availability and even tried calling the hospital with no answer and she said they sent a referral to the hospital Nov 12th and they thought the hospital contacted me already so she had a doctor call the hospital and it turns out the hospital thought I gave birth already and THREW AWAY my referral 😤 she also told me that the hospital didn’t have an availability for me and to stay by my phone for a call back to let me know what they come up with. So now I guess I’m just waiting on instruction on what to do next 😪

*** They finally called and told me to come Saturday on the 26th to be induced 😇💙👶🏻