Recently i have lower back pain and around my abdomen, if i push and couching its connecting to my back pain.now the pain is my right side abdomen too.

Pelvis: Look to the joints of the pelvis for pain that is aroused by low back movements that elicit discomfort in abdomen and low back. When a joint of the pelvis is loose, the abdominal muscles can be stressed to develop muscle spasm. Study the brighton criteria to gain insight about joint hypermobility syndrome.

Get checked: Clearly there is a progression of your symptoms which always should be checked out.