Why can't you sue someone for making you catch a cold or tuberculosis, etc?

You can sue anyone for anything, but two things are necessary. First, the burden of proof is on you to show that what you say is true. That may be more difficult than you think. You can testify to something, but you have to prove it with other evidence. You have to have your witnesses and records, medical records in this case. The fact that you became sick is not enough. You must prove that the sickness came from the other party. If you win the first part of your case, then you must prove your financial damages, same rules of evidence.