If you look and dress sensibly, and don't make a beeline for the alcohol then you'll probably be OK in LHR, though strictly speaking you do need to be over 18 years old. In MIA on the other hand I wouldn't even attempt entry at the Premium lounge. You could check with AA Club front desk for admission, clearly highlighting your age. I believe you are allowed in, but they need to ensure you are not served alcohol. And if they make it awkward then that's just the way it is over there until you're 21 years old.

And welcome to Flyertalk lgwflyer, welcome to the BA forum. It's good to see you here, I hope you have a good flight and you'll let us know how it went. You can also do some searching on previous examples of this, it's not the first time this question has been raised.