Hello,
There is a clinical entity known as coccydynia which matches your description to some extent.
This condition is believed to be a result of tailbone (aka coccyx) inflammation presenting with local pain or dull ache and sometimes with a tender point at the upper portion of the buttock cleft some distance away from the anus; which explain your discomfort when rocking backwards.
Coccydynia can develop spontaneously without any significant trauma to the tailbone although previous trauma to the surrounding area predisposes you to coccydynia. In this case, avoiding pressure at the tailbone by leaning forward while sitting may help.
Depending on individual, the discomfort should go away within a few months with or without pain killers.
As to the transient throbbing anal pain which you felt more on the right, local cause such as a small anal fissure with spasm could be the reason although anal fissure pain usually last more than 5min.
May I suggest you watch the discomfort and your bowel movement. If there is now a constant urge to open your bowel with the discomfort worsening or a significant change in your stool consistency or stool caliber, seek medical help early.
- Dr Quan