I gone through your question, but you have not given any nature of cut, size of cut, the suturing depending up on the nature and size of the cut. But your problem lies between the fingers, if the cut is small no need of sutures. For bleeding control you have to give pressure, if still bleeding continued you need to consult doctor, if you make late there is no possibility for suturing. only dressing is enough and use antibiotics and painkillers, vit c also useful to get speedy healing.