Is it possible to remove half lower wisdom tooth when infected and very close to nerve? to avoid possible nerve damage.

Contraindicated: if teeth with an active infection or pathology. See a board certified oral surgeon for assessment. Good luck!

Yes: Yes. Infected wisdom teeth are removed often. Always small risk of nerve damage. See oral surgeon for advice/recommendations.

Infected wisdom: These types of questions are best answered by a Board Certified Oral Surgeon who can clinically examine you and along with radiographs of the area discuss risks of surgery, treatment options and recommend what to do both before the surgery and afterwards should there be an unusual events during or after the surgery. Broad generalizations over the internet is not really helpful or fair to you.

Need exam: set up a consult with an oral surgeon to evaluate and discuss options

OS consult: Get a referral to an oral surgeon and a panoramic x-ray. The oral surgeon can best ascertain if it is prudent to extract the tooth and what the ramifications would be. I am sure you will be fine, third molar extractions are routine for oral surgeons.