In rereading what I wrote, I was thinking that the cut was on the back of your right hand.
You can check the temperature of the injured hand with the back of the opposite hand.
If the bluish color were due to low bloodflow, the temperature would be cooler than normal. That would not be good, and you would need to have your doctor check the wound. If the bluish color is due to bruising, the temperature would likely be normal, or warmer if the area is inflamed.
I hope that the laceration was thoroughly washed out before stitching.
Carol
Check the temperature of the injured spot with the back of your left hand, and compare it to the skin on your right forearm.
If it is as warm or warmer than the skin on your forearm, then it is getting enough blood circulation.
If it is cooler to the touch, that would mean that it is not getting as much bloodflow. The bluish color might be due to bruising, or blood under the skin.
Swelling and inflammation are normal after an injury like that. You should be elevating the hand as much as possible.
When you sit at a table, put your elbow on the table with the hand pointing straight up, or at least resting on a pillow.
When you lie in bed, put a pillow by your side, and rest the hand on the pillow, so that the wrist is higher than the elbow.
If you are standing or walking, put your right hand up near your left shoulder to raise it.
All this will help the blood and fluid to drain back to the heart.
How long is the laceration?
When is your follow-up visit to the doctor to get the stitches removed?
You probably shouldn't be bending the index finger much or making a fist, until the edges of the skin begin to heal together.
Carol