It's important you keep the wound clean as if it gets infected, infection can enter through blood into your system and lead to septicemia. Remove the bandage, wash with clean water first. If you can get sterilized water and wash it. Later wash it with butadiene or hydrogen peroxide. This will to an extent keep the area disinfected. After that place cotton, if you feel there is a particular vessel damaged, that is bleeding is occurring continuously, apply pressure on that area.
Following that, wind gauze around it. Keep the finger with bones I position, keep two scales against the dorsal and ventral plane and wind the gauze around it tightly. Try keeping in position as much as possible.
Visit a doctor as soon as you can as you definitely need suturing and reduction else your thumb can be deformed permanently.