Best ways to overcome my fears...

I would second some of the things other members posted here. My personal advice as a still novice ocean angler would be to take it slow. I set a goal to get my kayak in the ocean about 3 years ago and have 12 trips under my belt now.

Fear is a survival instinct, don't ignore it. I still feel too uncertain to do any solo trips in the Ocean, try beach launching, or fish in areas with tricky terrain or tides.  Over those three years, I have fished with a few kayak guides as well. I enjoyed a day in Santa Cruz with Allen (Bushy) and let him know before the trip all I wanted was to learn safety and get comfortable in the ocean, any fish were a bonus. Highly recommend doing that too

I would take a kayaking and surf zone class before doing anything else. You will learn how to read the swells and navigate them, about the different braces you can do to keep yourself from falling over, and how to self rescue. You will fall over countless times in class, and have ample practice bracing and self rescuing. By the end of the class, you will be much more confident in a kayak.

Only then should you even mess with a fishing rod on a kayak.

Where can I find a surf zone class?  Thanks in advance.

Try this:

http://www.hmbkayak.com/classes/surf-zone-and-wave-dynamics/

Where can I find a surf zone class?  Thanks in advance.

CCK has some great classes as well.  The nice part about these classes is that you'll use your kayak or one of their borrowed sit-on-top kayaks. 

https://calkayak.com/kayak-fishing/kayak-fishing-classes.html

Where can I find a surf zone class?  Thanks in advance.

Buy a skateboard helmet grab some yak fishing buddies, strip your deck and hit the surfing spots. It’s a blast and great way to learn how your boat handles in the surf. Best part is your planning on dumping so it’s no stress.