Yes, many have experienced groin pain in early recovery. At only three weeks post op, it is not unusual.
Your leg endured a controlled trauma, in a very small area. Your muscles, tendons, ligaments and other soft tissue is going to cause you discomfort and pain for a while yet. Take the meds for as long as you need to in an effort to remain comfortably mobile and able to rest easy. If you feel the prescribed meds along with regular icing is not effective, contact your surgeon's office to discuss having your prescription adjusted. Also, you can ice as often as you like, for as long as you care to, but when you do ice, don't ice for less than 45 mins per time, always placing fabric between bare skin and the ice source.
Wishing you comfort and better pain control. Stay in touch and let us know how your're doing.