Could you estimate how much projection(cm) I will need? Or which size of a chin implant I will need?

Thank you for the question and sharing your photo and concerns.  It is difficult to tell due to your position in the images, but if your chin is underprojected this likely could be improved with a chin impant.  I would consider evaluation by a facial plastic surgeon or other cosmetic surgery specialist to discuss your options."This answer has been solicited without seeing this patient and cannot be held as true medical advice, but only opinion. Seek in-person treatment with a trained medical professional for appropriate care."

 The chin is a three-dimensional structure, so a full set of pictures are required  before making any determination of what may or may not be needed to augment the chin. Chin implants are manufactured in a variety of sizes and shapes, are composed of Silastic  and are usually placed through a submental approach under local anesthesia as an outpatient surgical procedure. It  is best to determine the size of the implant at the time of examination and consultation.

Being an option, chin implants or fillers have serious disadvantages, specially in
the mid and long term, patients are rarely happy with them after 5-6
years, all are out by then or later.Consider the chin advancement by means of sliding genioplasty, the advantages are:-lifetime procedure, no more revision or renewal procedures-more natural than implants-no visibility of implant edges during gestures-improves
the double chin effect at the sub-mental muscles (floor of mouth)
hammock caused by lack of tension there; also improves the shape and
tension of perioral muscles; implants do no offer this feature-horse-shoe enhancement, covering the chin and also the jaw sides of it-no future displacements or neuritis of mental nerves-practically zero infections and 100% healing of bones-no
need for complex plates and screws that may need future removal; just
steel wires synthesis may suffice, they stay buried into bone callusThe cons are:-expensive, but cheap if you consider the lifetime pros-technically
demanding, few surgeons are experienced or comfortable (though I
personally perform 100% of the chin augmentations by this osseous
method, always after offering the patients both options)-scary for the patient (though not so much if you explain well the stuff around it)This
is my advice to patients with weak chin, the sliding genioplasty above
all other options. After explaining pros and cons all my patients opt
for the osseous genioplasty and opt out implants or fillers.