"I'm feeling under the weather." - This is a common idiom! "I'm coming down with something" or "I have come down with something." "I caught a bug." - "Bug" is slang/a colloquialism for a virus or a cold. Hope that helps :)

"I don't feel well" or "I'm not well" are standard expressions for saying you are sick. "I don't feel 100%" is a way of saying you feel "a bit sick", while "I feel terrible" is another way if you feel even worse. "I feel wrecked" is a slang way of saying you feel ill more because of tiredness/lack of sleep/partying the night before/hangover rather than an actual illness. Edit: My mistake ! Sorry, I thought this was an English question.

どういたしまして。

うえださん、ありがとう。

As you guessd right, there are many other ways to say in Japanese that you are in bad health. So many that I would like to give you only a few of them here. / 病気である、調子が悪い、体調が悪い (悪い or 優れない) 、具合が悪い、吐き気がする [When you feel sick, I mean when you have nausea, you specifically say this way.]、気分が悪い [It might more often mean you just feel bad even if you are in good health.]