When you have a disease, we say 'Tengo una enfermedad' or 'Estoy enfermo', which is more or less the same than in English. When you feel ill, something like a cold, we say 'Estoy malo', 'Me encuentro mal'. The concept associated to 'Tengo una enfermedad' is related to something more serious, permanent or, at least, for a long period of time. The concept associated to 'Estoy malo' is related to something not that serious like a cold, a headache or sore throat. So you can feel fine at that moment but still having a disease. Translated to Spanish you can say 'Estoy bien, pero ...' (as Cin said before).

You are not "sick" in the bottom of my heart. So I would like to hear that you say fine to me and see a smile on your face. Have anice day! BTW, I am ok.

You can say something like "Estoy bien, aunque algo enfermo" o "No me siento muy bien de salud". In general, people ask "How are you?" as a social elicitation to which you always have to answer "fine", no matter if it is true or not... So for me is better to answer "Estoy bien, pero..." and then tell the other person that you are sick :)

希望你早日好起来，还记得我是谁吗？

Estoy enfermo, pero bien. Estoy enfermo, pero me siento bien. Estoy un poco enfermo, pero me siento bastante bien. Me siento bien, pero estoy enfermo. Me siento muy bien, pero estoy enfermo.