Trimmed nail too short Help

She didn't even flinch didn't notice it no tears thankfully but Now it's bleeding a little but won't stop and she's 20 weeks so her hands are always into her mouth she keeps fighting me on holding cotton pad to it and I read I can't use a little bandaid. I tried a burp cloth a wipes rinsed it under cold water She's happy and fine minus getting annoyed with me holding her finger and she keeps squeezing which makes it bleed more. Help ! I just wrapped it in Kleenex and put one her 0-3 months mittens on it and nursing her and hoping she falls asleep. It's been 15 mins already