That kind of short distance driving usually requires more maintenance, not less. If the engine never gets up to full operating temperature, the oil gets more contaminated than if it reaches full temperature on a routine basis.
This Civic uses 10W-30 transmission oil, and I seriously doubt it is leaking or that low oil is an issue, but draining and refilling the transmission oil couldn’t hurt, and it could give you some peace of mind that you’ve ruled it out.
Just so you know, you have three options for changing the transmission oil on this car. You can use Honda Manual Transmission Fluid (which is probably - based on the price - synthetic 10W-30 oil with some additional additives), you can use synthetic 10W-30 oil (which is what I do), or you can use regular 10W-30 oil, but you should change this oil more often than you would otherwise, at least every 30,000 miles. I believe the manual transmission on your car holds 1.8 or 1.9 quarts of oil, so you only have to buy two quarts, which will give you enough to fill it up all the way until some pours out of the fill hole.
As long as you get more than 1.5 quarts of oil when you drain the transmission, you can rule out transmission oil as the issue, but you might as well go ahead and drain and refill it. Once you remove the fill plug to check the level, you’ve done almost half the work of changing the oil. There is no filter to change.
Like others have said, it’s probably the clutch, not the transmission. The clutch is a wearable part, so if this one lasted 18 years, the car is due for a new one. I suggest you pay a little extra to get this clutch job done at a Honda dealership. You don’t want an independent mechanic or a chain operation to put in some aftermarket clutch that doesn’t perform as well as the one a Honda dealership will install. Don’t skimp on this job. Get the entire clutch replaced, including the flywheel. You might even consider letting them replace both the master cylinder and the slave cylinder to ensure everything will behave as it should when the job is done.