Sounds like your right side is carrying the load, and may be pushed a bit.
If you're concerned at all about the implant, if you can - have xrays done and reassure yourself that it's in good shape. It most likely is, probably your right is just doing a lot of work.
If it's groin pain, it may be the Illeopsoas muscle(s), which start at the lower back (blue) and go through the hip to the groin (blue and red), to the outside of the thigh connected at the knee (green).
This set of muscles can become irritated, shortened, etc. with a hip procedure and takes special attention to keep loose or get relaxed. They are also an issue for runners and other sports that rely on that area.
Some things you can do to help the irritation:
- Use a styrofoam roller. These are not expensive at all, and can be applied to the outside of the thigh and the lower back to calm down the IT band (green)
- Use a tennis ball to massage the groin and lower back. For the lower back, I just put it between my back and a wall, lean back and roll it around the affected area (avoid the spine).
- Do core exercises as well as the others you're doing to get those muscles stronger.
Good luck, I hope it clears up.