It sounds like you have chalking that needs to be, at the very least, polished out.
Polish is not wax, and wax is not polish.
If you hire someone to correct the finish on your boat that tells you they are the same thing, hold on to your wallet and run quickly away.
Wax is really just a protective coat. Some waxes are "Cleaner Wax", generally meaning they have a solvent content in them that will clean off some light stains or loosen dirt. Garry's is a popular "Cleaner Wax" that a lot of boat guys use. I use it myself for in between stuff. It will probably clean a chalky finish and make it shine temporarily, but it doesn't correct the problem and the chalking will re-appear when the Garry's wears off.
Polish is not a wax. It is a diminishing abrasive. It is a gentler, milder, finer version of compound. The next most aggressive thing after a compound is wet sanding.
Once you wet sand, you need to compound out the marring that the sanding causes, and then polish out the area you compounded to bring out a clear, clean shine.
The last thing you do is coat it with a wax, or a synthetic sealant, designed for use on boats, to protect the finish. Your choice. But you MUST protect the surface with one or the other. If you don't, the UV Rays and other elements will destroy your finish. There should be no need for a "Cleaner Wax" after you polish because the surface should be clean.
The golden rule is to always start with the least aggressive method when trying to correct a finish. That would be polish. If polish doesn't take away the chalking, then move on to compounding, if that doesn't work then, it's time to wet sand.
You will need a good rotary (not random orbital) machine, and the appropriate wool pad. There is a wool pad for polish, and another more aggressive one to use with compound.
Random orbital machines are fantastic for cars, I have two good ones that I use frequently myself, but they are no match for the tough gel coat on your boat.
I have a Makita 9227 rotary that I love and highly recommend. But, I do my boat myself, and detailing cars is a hobby of mine. I've heard of others who are just occasional users that have had great success with a cheap rotary from Harbor Freight, but I have no experience with that machine.