These two phrases sound very similar, but unfortunately they cannot be used interchangeably since they have different meanings. Let's have a look at some examples:
I always do
We use this when we want to talk about something that we do every time.
"I always go to work in the car." (not 'I'm always going....')
"I always brush my hair in the morning." (not 'I'm always brushing....')
"I always read my child a bedtime story." (not 'I'm always reading....')
I'm always doing
Rather than using this to express what we do all the time, we use to to show that we
do something too often, or more often than we think is normal.
"I'm always losing my keys." The speaker doesn't lose their keys every time, just more than they think is normal.
"David is always watching the television." David doesn't watch the television 24 hours a day, just for a longer time that the speaker thinks is ok.
"You're always leaving the lights on." The person doesn't leave the lights on all the time, just more often that they should.