Hello from JustAnswer.
It is certainly true that a muscle strain can cause pain, stiffness, and limited range of motion, but there are other possible causes, and the most common other condition would be degenerative changes in the hip. Pain from the hip is frequently felt in the groin. Degenerative changes are still considered a type of arthritis, but there is less active inflammation than with other types of arthritis. There are also a number of other less common conditions that would need to be considered for persistent pain, stiffness, and reduced range of motion, such as problems with blood flow to the hip, although doctors will typically first evaluate for more common conditions. An exam and/or a plain x-ray may be sufficient to clarify the cause, but advanced imaging, such as an MRI, may be needed in some cases.
It is reasonable to first try to manage this at home with local care and anti-inflammatory medicines. Ice is the most important local care initially, but after a few days, moist heat also can help. Ibuprofen is a good anti-inflammatory medicine, but different anti-inflammatory medicines may work better for different people.
If the symptoms had just started, it would be reasonable to plan for a trial of home treatment and only see your doctor if the pain persists. However, since you have already been using good home interventions for 2 weeks, it is at a point at which it would be appropriate to see your doctor. It is not necessary to be seen emergently and until you can be seen, it would be fine to try the addition of moist heat or a change to naporoxen, the only other anti-inflammatory medicine that is available over the counter.
If I can provide any additional information, please let me know.