Mine is sitting a millimetre plastic to plastic too.
I’m sorry to say your soldering does look a bit iffy. Was you iron hot enough? You can actually do more damage to a modern pcb if you take too long to make the joint because the tip temperature is not high enough to get the lead and the track up to temperature so that the solder flows smoothly and quickly.
It’s hard to know what to tell you to do, other than practice on something it doesn’t matter about. If I was checking that connector, I’d use a soldering iron and solder sucker to remove the excess solder (there’s far too much, it should form a meniscus up the pin like coffee up the side of a mug), and the surface should be smooth and shiny. What makes me think your iron was not hot enough is your joints look dull and pasty, and it looks as if the ball of solder is sitting on and hasn’t flowed around the pad. The 6 pins on the left have got the right amount of solder on.
Here’s a GLCD I soldered up a good few years ago:
It might be worth watching the video just past half-way down this page:
https://learn.sparkfun.com/tutorials/how-to-solder-through-hole-soldering/all
Here’s the direct link:
