Yes, it is maxed out.
The 1988 9.9 used Merc's 12 cubic inch block which it shared with the 6 and 8 horse. The 15 horse used/uses a 16 cubic inch block. Midway through the 1994 model year, they started building the 9.9 with the 15 horse blocks - so 94 1/2 and newer 9.9's can be upgraded. You must swap the carb plus the exhaust plate/tube. However, if you live in the U.S. that is illegal (minor detail).
So no, you can not convert "your" 9.9 to a 15 - not the same powerhead.
On a side note. I have a 14' aluminum (boat weight with engine 280 lbs). I sometimes run in lakes that have a 10 hp max. So while I normally have my 15 horse fitted, I also own a 9.9 that I swap out to make it legal on those lakes. While not scientific my "own testing" has shown a whopping 2 mph increase with the 15 over the 9 horse (and I don't know many who can tell the difference between 19 and 21 mph unless they are looking at a hand-held gps).
So if you want a performance increase that you will actually notice - get rid of your 9.9 and go with a 20 or 25 (if your boat can take it). Trying to squeeze a few more horses out of a 9.9 will only leave you with less money in your wallet and no "noticable" performance improvement.
For others that may be reading that have one of the newer 9.9's that can be converted (serial 0G760300 or higher), a carb goes for about $230 plus a couple bucks for a gasket. The exhaust plate and new powerhead base gasket will run you another $85 bucks (so we are up to $315 plus tax). The change will take a couple hours of your time plus 35 bucks for a Seloc's manual to show you how to do it.
And in the end for about $350 bucks you might see 2 more mph - you have to ask yourself if each mph increase is worth $175 bucks.
I also mentioned in the U.S. it's illegal. Here's the directive -
"EPA regulations prohibit changes to engines that could affect emissions limits. Per the service manual, "The dealer and/or consumer is not to modify the engine in any manner that would alter the horsepower or allow emission levels to exceed their predetermined factory specifications." The only changes permitted are carburetor jet and gearcase/gear ratio changes for high altitude operation as detailed in applicable Mercury Marine Service Manuals."