This is off the top of my head and I should be able to tell you being a Yorkshireman, but living here I take things for granted a bit. I THINK that Humberside as a county ended a few years ago due to the constant whinging by us Yorkshire folk! Having said that, I still see references to Humberside when I travel over there from Leeds. I am a bit confused and I live here! I should have done a google search before typing this and then we would all know exactly how things are.
East Yorkshire became Humberside after some government initiative (forget which year but a couple of decades ago) there was never any north or south Humberside, just "Humberside" which was plugged as the newest county in the UK. Anyway the people of Humberside moaned of course and said they preferred being part of Yorkshire so a few years back they changed back to being East Yorkshire. so the answer is that Hull is in East Yorkshire. Correct sft, Lincolnshire is the south side of the river Humber.
to be pedantic - it's now called the East Riding of Yorkshire - according to the powers that be. However, I was born in East Yorkshire and still live in East Yorkshire - (the address on my letters omits the Riding.) despite the years in between when THEY decided to rename it North Humberside.
I think it is confusing though, because there are still so many organisations with Humberside in the name, such as Humberside Police - they have been in the news a lot recently.