Bone/tooth fragments after extraction?

i had my very back tooth out mid december. aside from an infection which was treated with anti-b’s the hole is healing fine, However I noticed a sharp bit on the side of my gum about a week ago and I picked at it and eventually i got a teeny bit of sharp material from it(btw know i shouldn’t pick but I couldn’t help it) anyway i now have a other sharp bit in the same place and it’s sore. can anyone suggest how to help work itself out of my gum quickly?

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