Right rib clicking when pressure is pushed on the edge of rib cage and sometimes with a deep deep breath, is this normal?

? costochondritis. Costochondritis is an inflammation of the junctions where the upper ribs join with the cartilage that holds them to the breastbone, or sternum. The condition causes localized chest pain that you can reproduce by pushing on the cartilage in the front of your ribcage.
X-rays. You could have a subluxation at the juntion of the rib articulating either with the sternum or with the cartilage that bridge the space between the rib and the sternum.Proper imaging is necessary in orther to make the proper diagnosis.