Doctor has had letter but I haven’t

I had my ESA assessment interview 4 weeks ago. At the doctors yesterday they showed me a letter they received 2 weeks ago from DWP saying I had been granted ESA and they no longer have to send sick notes to them (dated 20th March). I’m yet to receive anything though.
I haven’t been receiving any payments so far (not even assessment level) due to (after a lot of phone calls) not enough NI contribution payments in 2016. Again after many hours on the phone HMRC said if I paid the shortfall I “should” qualify. I queried this again with DWP before I made the payment and they said that “it depends” as HMRC may fine me for late payment (how can I be late paying something I didn’t need to pay?!?). I paid it anyway- was around £50. I’m still none the wiser as it where I actually am.
I have worked all my life- went part-time in 2016 due to health issues. This process has not helped with my mental health issues
I’m not sure what I’m expecting in way of response on here but I was wanting to get it out and maybe get some reassurance