David, this is well beyond the first aid kit. But, if you have had any serious bout of AMS, and if you intend to make fast ascents comparable to Rainier in the future, you might want to have a talk with your physician about a prescription for Diamox.
If you are making normal ascents to high elevation, and you are taking normal time to adapt, then you probably don't need it. However, some people have a susceptibility to altitude, and they don't want to keep having their trip screwed up by any serious symptoms, so they take Diamox, starting a couple of days in advance.
I've carried the stuff several times, but I have only used the stuff once, and that was for fast ascent at much higher elevations than Rainier. For most, there are some mild side-effects. Talk to your MD.