Before wudhu, I always wash my hands and face first. One time, after washing my hands and face, I started my wudhu, when I was about to wash my left hand, I found my small wound bleed again (on my pinkie under my nail) but then I just continued my wudhu, but I made sure it didn't touch my right hand, I just washed the wound after I wiped my left hand with water on my right hand (as a usual part of wudhu act)
then the bleeding was stopped. Is my wudhu valid?

Your wudhu is valid