Blowing noses? Isn't that what you're complaining about? Or just sniffling? If someone's sick with a cold, they're going to be doing a lot of both. It's not like you can blow your nose once and be good for the rest of the day; if it was like that, then you wouldn't have coworkers sniffling all day long. People get sick. Deal with it.
As for tapping fingers, how's that any more annoying that key clicks, foot tapping, or constant movement? People do all those things too. The fact is, people move. They cannot sit perfectly still and use the minimum necessary motion. Deal with it.
You're asking for people to be super-human. That isn't reasonable or possible. People are what they are, so you need an environment which accounts for that. If you don't have that, then it's management's fault, not the peoples' fault for just being what they are.
Honestly, you sound like someone complaining about cats licking their butts and dogs drooling.
You can predict that you will be talking on the phone if you are making a call (such as scheduling a doctor appointment). You can walk to a phone room when you receive a call.
By then, it's too late: you're now disrupted by the noisy phone ringer, and the start of the conversation.
And what if the phone room is occupied? If the company is really cheap with space, they probably didn't put enough private rooms in to satisfy demand.