Can I say "Ich bin gut"?

You can say Ich bin gut grammatically and a German will understand your words, but you almost certainly should not say it if you mean to say I'm doing well or I'm good in English. In German Ich bin gut does not mean I'm feeling good, it means I am a good person morally, or I am talented or good at something. For example Ich bin gut in Englisch means I am good at English, or Ich bin ein guter Mensch means I am a good human. If someone asks Wie geht es dir How are you, answering Ich bin gut sounds like you are saying you are morally superior or you are bragging about your skills, which sounds strange and even a bit arrogant to native ears. What you want to say instead is Mir geht es gut which literally means to me goes it good, or simply Gut, danke meaning good thanks, or Es geht mir gut. The reason learners make this mistake is direct translation from English I'm good. German uses a different structure for wellbeing. The only situation where Ich bin gut alone is natural is when you are contrasting with bad, like asking Bin ich böse Am I evil, and answering Nein, du bist gut, ich bin gut. So for everyday small talk avoid it and use Mir geht es gut.