Lip filler can be done with a canula, which is less likely to injure blood vessels, this is passed along the lips from the side.
My recommendation would be to get a consultation with an experienced Doctor so they can examine and palpate the lips to assess where the blood vessels are. They can...
I am sorry but it is too early to have your lips injected with filler at this point. You need to wait about three months to see how the scar from the bit looks and then you will be able to assess it. Your lip fillers will be more complicated because of scar tissue so please consult a board ...