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There must be a local lesion which is causing the problem of recurrent bleed.
It can be an eroded area in the tooth which is causing a bleed or a friable polyp, or a local ulcer or an ectopic patch of endometriosis
in case of females when it typically bleeds corresponding to periods.
Any local pressure for a period of 10 minutes would stop most of the bleeds, you do not need seek a tea bag for putting pressure to stop bleed.
Even pressure with bare finger/handkerchief is also effective to the same extent;
So next time do not run/wait for tea bag to stop bleeding.
Just put a local pressure at bleeding point.
Consult an ENT doctor for a local examinaion to detect the exact cause of bleeding.
If you have any further query please let me know I would try to answer it for you.
Wish you a great health!