Hi Tony,
This is definitely a very interesting topic. I'm sure research has been done, though I haven't been able to find any scientific papers on it yet, though I'll keep looking for your benefit. Wikipedia, though of course not 100% accurate, does provide a pretty solid background on it though:
http://en.wikipedia.org/wiki/Ginger#Medicinal_use. At least, it is not clear exactly what the ginger does: does it actually affect the virus, or does it merely deal with the symptoms? At any rate, as a molecular bio major (and an aspiring virologist), these kinds of questions get me somewhat (in a rather unfortunately nerdy way) excited.
The difficulty that you mention is a very complex one. Yes, as a high school student, it is unlikely that your high school has the necessary equipment to qualify to receive active rhinovirus (typically, at least biosafety level 2 would be required, this is generally only present at university labs and other research facilities). My first thought is that, if you want to pursue this exact method of testing the effect of ginger on rhinovirus, you would have to be in a university lab. So, if you are motivated to do that (and by all means consider it! University labs are rather chill and good experiences), feel free to email professors at nearby universities and research facilities with a detailed research proposal and request to use their lab. Hopefully, a lab will be nice enough to take you on.
Now, a second difficulty that I also forsee is the effect of the immune system. Say the ginger actually affects some aspect of the immune system, allowing it to deal better with rhinovirus. So, if you proceed with the above route of joining a lab, a negative result (meaning that the rhinovirus is not inhibited by the ginger) may not tell you too much since it does not tell you how the ginger is / isn't affecting the immune system. However, if you do get to a lab, one possible further route would be working with mice. This has its own difficulties since only mammals normally are infected with rhinovirus. However, semi-recent advances have allowed researchers to use mice (this is quite cool:
http://www.nature.com/nm/journal/v14/n2/abs/nm1713.html and
http://www.independent.co.uk/news/scien ... 77668.html; the first describes a rare strain of rhinovirus, transgenic mice, and induced exacerbation of the airways, and the second describes just more of the transgenic mice). At any rate, though this is difficult, most labs (if they are very interested, and many labs are) can do this kind of research.
Ok, so on to joining a lab. Just some tips. Like I stated earlier, email professors with a specific, clearly defined research proposal (you don't obviously need the details of each method, but keep it clear what you aim to do and via what methods). Choose to email professors who are closely related to your topic, so generally virologists and the like.
Cheers! Hope this helps,
Aaron Lin