Suggest Remedy For Deep Cut In The Hand

im 45 male good health. if a drinking glass broke while my hand was inside trying to wash it. the twisting motion cut my index finger at the knuckle down the side towards the thumb removing a piece of skin about 1 cm. I was able to close it with a butterfly pulling the knuckle skin down the side to meet the other side of the hole. obviously the the right thing for me to do was to see a Dr. but thats not possible for me atm. so is this the right thing to do or should i have just covered the hole and let it heal on its own? normally i wouldnt ask a question like this but the size of the hole im closing and its location being more on the side of the finger where there isnt alot of extra skin has me wondering. please just give me an answer to this hypothetical question as i cant hold you liable. Thank you for your time.