Starting at 2nd level, you can add half your proficiency bonus, rounded down, to any ability check you make that doesn't already include your proficiency bonus.
I could at level 2 add half my proficiency (being 1) to for example Deception making that skill go from 5+1=6.
Now at level 3 I get to add proficiencies and decide that Deception should now be something I am proficient in.
The way I interpret this is that I could keep the 6 and add the 2 from the proficiency because at the time of adding (Jack Of All Trades) I hadn't been proficient in it.
So I'm just asking for clarification.