Good advice thus far. The stress of the trip, and of your first true ocean dives, can make a
big difference in the degree of anxiety you feel. I will focus on a couple of items that you mentioned. But, first things first:
Edit; The big reason I was feeling conflicted was whether I should go on the deeper boat dive before getting a better grip and/or adjusting to this new environment closer to the shore.
You are right in feeling conflicted. I would recommend
against going on any boat dives until you resolve some of your issues. Yes, you might find that today is a brand new day, you do a boat dive and have a blast, no issues clearing, etc. That would be great. But, you might just as easily find you have the same issues, can't descend with the group, feel frustrated, feel embarrassed, etc. And, that wouldn't be so good.
[The beauty of Bonaire - you don't
HAVE to do
ANY boat dives to have a great dive trip. There are plenty of terrific shore dives available. You don't mention the resort - from your description I was wondering if you are staying at Buddy Dive. If so, the 'house reef' is simply superb. (Frankly, the same can be said for most of the resorts on Bonaire, in fact).]
Buoyancy and weighting: as several have mentioned, you are diving in salt water. You will need more weight than you needed in the pool, with the same exposure suit. Also, are you wearing more neoprene than you did in the pool? The anxiety of going into the ocean for the first time can definitely contribute to a wee bit of hyperventilation, which accentuates the buoyancy problem. (The shop owner's advice to 'practice exhaling more' suggests that this is a factor.)
Equalization issues:
I seem to more difficulties equalizing my left ear (the one that got sore/painful after my first lesson).
This comment concerns me a bit. You are saying that one ear was actually sore after your first pool dive? What kind of pain? How long did the discomfort persist after that first session? Did it recur? Was it worse when you were trying to clear?
Also, I would like to know if there's a better way to determine if your sinuses/ears are ready for your dive.
Possibly.
There are more than a few walk-in medical clinics in Kralendijk. It would be worth considering a visit, today. (Ask the resort staff for a recommendation.) Have someone take a look in your ears - particularly the left - with an otoscope. What happens with your tympanic membrane when you do a valsalva? Does it move outward normally? At the very least, a 'negative' evaluation - no issues observed - would provide reassurance. I have done this more than once after a dive trip left me with pain / discomfort.
You have spent considerable money, and time, to get to the 'Diver's Paradise'. But, don't let the stress of feeling like you MUST dive, in order to justify that expense and time, cause you to do something that will really make the experience unpleasant. Even if you have to spend another day getting ready - a walk-in clinic visit. or more time in shallow water making sure you can equalize, or trying another mask, etc. - it would be worth it.