its a tricky one. if i have the choice between taking something and being really sick, or not, i'll take it. you have to find your own line that you're happy to walk, and decide where your own cut off point is.
are you talking about the fact that medicines are animal tested, or contain animal products? i take an antihistamine daily (my life would not be very nice without it, in my opinion) which comes in a lactose free liquid form so is animal product free (took me a while to find it, lol, but i did) so there are some drugs around that don't come in a gelatine shell or contain dairy and or egg derivatives.
you could always consider trying to ethically balance the choice to take a not 100% vegan medicine by being proactive in trying to change the laws around animal testing, and contacting drug companies to request they consider swapping lactose for sucrose as a filler in their drugs, and swapping gelatine shells for cellulose, that way you're trying to change the situtation for the better.
you could also look into your local health food store, or into finding out about herbal, homeopathic, and non mainstream medicines for things like allergies or colds, there are plenty of things that can help that don't come from the doctors office or the local pharmacy.