Ted is correct that this is almost always a problem with the trim limit switch rather than the switch on your throttle handle. Sometimes a bad solenoid can also cause trim control problems, but in the case of raising the drive, a bad solenoid would also interfere with the trailer button working correctly. Since the trailer button works, but not the trim up button, the trim limit switch becomes the most likely culprit.
There are several ways you can handle this.
First, you can ignore it and just use the trailer button to raise your drive. This will work just fine, although your 'trim up' button on the throttle won'w work and you won't have any protection against accidentally raising the drive too far while the engine is turning the driveshaft. Raising the drive too much under power can problems with the U-joints in the outdrive. (The U-joints will make some noise when you trim too much under power, but it's best not to get to that point. Raise the drive too far while the engine is on, and you could trash your U-joints.)
Second, you can disable the trim limit switch pretty easily. There is a bullet-plug connection between the wires going thru the transom to the trim limit switch and the wires to the controls on your throttle. A very simple homemade jumper can be used to eliminate the effect of the trim limit switch. This allows your 'trim up' button to work but without any protection against trimming the drive too high. In essence, with those wires jumpered, the trim up button will function exactly the same as your trailer button, and with the same risks if you trim too high.
Third, you can replace the trim limit switch on the outdrive. This really requires some disassembly of the transom assembly and is easiest to do when you're having your bellows replaced (which most people do occasionally anyway).
I chose to bypass the trim limit switch using a homemade jumper and then I just replaced the trim limit switch a year later when I had to do the bellows. If your trim gauges works and you're careful not to raise the drive too far, it works fine. (In fact, some guys just jumper the connection and leave it that way permanently.)
Hope this helps!