You've gotten a lot of good feeback. I had a limp on both sides until about five, maybe six weeks.
Then I got it back every time I did something new (after I did it). I think it's just part of getting your muscles back into the game. My PT folks devised all sorts of fun and interesting things to strengthen my small muscles.
I could see them giggling to each other as I walked in (I was their first HR patient, so a good lab rat); it was quite unnerving. Leg lifts, clamshells, etc. will get your hip muscles stronger, but it is an evolutionary thing, you have to respect the healing of the bone that is going on as you rebuild the muscles around the joint.
In due time, the limp will go, but you may get clunking of the joint, which I think is also associated with muscle strength of the minor muscles.
Patience goes a long way here, at three weeks you are very early in the game.