Ok...just chiming in as a resident kidney expert. (Long story...but my youngest DD has been in renal failure since age 2...just had her left kidney removed a few months ago...ergo I am walking encyclopedia when it comes to kidneys and UTIs, etc.)
This sounds more ovarian cyst-ish to me. Especially since AF left 9-10 days ago...that would be the time when an "innocent" cyst shows up. And you may very well have had many since age 15--the vast majority of ovarian cysts go undetected b/c they cause no problems and go away on their own.
Depending on what you are doing for exercise, this could be part of the issue as well. There is a slight chance it could be referred sciatica pain. Now normally, sciatica would be lower back pain, down one butt cheek, and down into the back of the thigh...but when the pain is referred, you feel it in the front. Still, though, this would be unlikely.
Not likely to be appendicitis (which would account for the lower right abdominal pain) as that is usually sharp and VERY painful. However, the best test for appendicitis is....take your hand and put pressure on the area where it hurts....keep the gentle pressure on for about a minute. Then remove your hand. If the pain is WORSE when you remove your hand, then it is likely appendicitis.
Let us know how it is later in the day and again in the morning. Is there a time of day when it is better/worse?
How long have you been on the pill? If over 5 years, your body may be ready for a change. However, I doubt you are spontaneously ovulating.
In any case, I hope you feel better!