I would talk to the co-worker and find out what the story is. If the condition is truly medical and chronic, chances are she is aware of how her cough could make people feel uncomfortable and she's probably embarrassed about it. If you bring it up in a light-hearted but concerned way (concerned for her, not for you) then it might clear the air, so to speak, and maybe you can all come up with some sort of solution. On the other hand, some people are truly not aware of how their personal behaviour can affect others, but in most cases, if you bring it up in a non-confrontational way, they will become aware and will try to address it so that everyone is a bit happier. Coughing/sneezing/spluttering and otherwise orally/nasally ejecting fluid/spray is not great for others' health and it's not unreasonable for people to be concerned by it. It is however important that everyone acknowledge an element of compromise will probably be necessary (as is usual).
I would not recommend that you participate in a group-whine about this co-worker with your non-coughing colleagues. That sort of behaviour, where you form teams against a person (at my work, I call it clumping) is not healthy and is honestly quite childish - 'everyone' b****ing about so and so, it's gross, yuck etc etc etc' - it's not appropriate behaviour in a group of adults and joining in or even allowing it to pass unremarked implicitly gives your consent to it and allows it to persist. None of it will get you or any of your co-workers to a solution and it just allows b****y people to be b****y instead of helping.
Best of luck, it's not an easy scenario to be in. I have a couple of staff at work who have colds at the moment and I just keep it upbeat, remind them to cough into tissues, wash hands, use antibacterial wipes etc. None of it is chronic though, so it's a little different to your situation.