We are sorry to hear of your injury and wish you a refuah shleimah!
If there is very little visible glue on the surface of the skin and it will fall off on its own, you may immerse as scheduled.
However, if the glue is not just in between the detached fingertip and your finger but all over the fingertip, unfortunately it is considered a chatzitzah and you have to wait until it comes off to immerse.
Please feel free to get back to us with any further questions.
BHatzlacha!