You used it correctly. "Workout" is the noun, and "working out" is the verb form. I'm doing my workout. I'm working out.

Hi Young! Good question. When referring to doing exercise in English, we use "workout." For example, "I am going to the gym today to do a workout" or "I'm doing a cardio workout tomorrow." If you want to say it in its "ing" form, then "I'm working out at the gym" is also correct. We separate the the two words - work and out (i.e. work out) - when we are referring to something needing to be fixed or sorted out. For example, "there is a scheduling problem, we need to work out a solution." Hope this helps :)

If you say that "I'm working out" it means you're doing your work outside. So, Correct sentence is " I'm doing workout"

it is workout and working out