One day I decided to actually EAT hot chocolate POWDER and I only ate like half a teaspoon and I felt some of the powder go down my throat and I started coughing afterwards that. Is there a chance that it went in my lungs :(?

There's a chance.

But it likely isn't anything to be too concerned about ... We inhale lots of particles (dust, pollen, pollutants) every day.

If you're still concerned about it, you could go to your doctor and have an x-ray done of your lungs.

The body is capable of removing such small particles from the lungs on its own.

If you did inhale some, it was probably an insignificant amount.

If you don't start feeling better in a day, you might want to call your doctor.