Hello and most welcome to HCM,
First of all i want to say that i have went through your description over and over. I must say that your concern is genuine and as a parent, seeking immediate help is most important for caring your child.
Anyway, your daughter put cotton bud accidentally into her ear, now, i want to know if the cotton left inside or came out with it ?? Whatever be your answer, please let me explain both -
* If cotton bud left inside, it has to be removed or else it will cause infection
* If the bud is ok and cotton not left inside, get your child TM (tympanic membrane) checked by a local ENT specialist
Now, you may ask me .."why" ???????
My answer would be -- because blood is coming out of the ear.. Now, what might cause that blood come out is, either it may be injury
to EAM (External acoustic meatus) OR to the TM (may be perforation) as child TM is very prone to injury due to short and typical angulation of EAM compared to adult. If it is TM perforation also, no need to worry as TM heals soon, provided it is kept dry by protecting from water entry during bath and preventing any upper respiratory infection
OK ...OK..., i think i should stop explaining more on it as you might start worrying to much.
Finally, my straight answer to your question... "shoud i go to the emergency or go to pediatrician"...?
Ans: To NONE of the above.
Please get your child checked straightly from your local ENT specialist and that too as soon as possible. Trust me..that would be the BEST.
With this i sincerely hope that i could at least ease your worry and guide your concern. I wish your daughter a very very early recovery and a very healthy life head.
Take care of yourself so that you can take of her.