I could be wrong - and I'm sure you will all correct me

- but I think the last hour of the flight no personal items are able to be out (must be stored away). Is this correct? I thought this was the "new rule" since the 12/25 fiasco. If that is the case, it might change the advice we give on what to do with children on flights.
You are wrong. That was a temporary measure which has already been lifted, and even while in effect applied only to INTERNATIONAL flights heading to the USA. I gather this poster is not flying from outside the USA.
I also have a child who gets hyper on Benadryl. Not something to try without doing it at home first.
For ear pain for a one year old, I recommend a sippy cup with a valve that is hard to suck from filled with whatever drink you know your child loves and will "work" for. Buy this drink once you are through security of course.
Personally I preferred NOT to use a carseat when I had toddlers. A car seat puts there feet out far enough they can kick the seat in front of them and then you have to worry about trying to stop that on top of everything else. We found the novelty of sitting in a regular seat belt and the flight itself (watching the beverage cart comming down the aisle, opening and closing the window shade, etc) was a pretty big distraction in and of itself on our kids' first couple of flights as toddlers(both flew about 6-8 roundtrips a year).
I advise against preboarding. This just adds time to sit quiestly. Wait until the very end and board last. Also, while waiting at the gate play active games like ring around the rosie, simon says, head shoulders knees and toes, etc. Anything to get the wiggles out.
Otherwise, better than any specific toy is being "ON" during the flight. Pay full attention to your little one and play lots of fun finger plays, make the air sickenss bag into a puppet, etc.
For specific items to pack:
My kids liked post it notes on flights at that age. They would go through a whole pad in about half an hour by scribbling on a sheet, sticking it to the window or tray tables and then doing the next page.
We also got a lot of mileage out of cheerios and fruit loops in a container with pretzle sticks and licorice stings. The kids would "string" the cereal onto the pretzle and licorice and then eat their creations.
Another good thing (for about a half hour when mine were toddlers) is a roll of masking tape. They were fascinated by the stickyness and messed around for quite a while with the stuff--until it ran out (with Mom playing along and being equally fascinated of course--also watch to be sure they do not tape their hair!).