Usually it is no big deal, but if you have discoloration, along with the numbness, it would not hurt to get a doctor's opinion. Always best to be careful with injuries, rather then just assume its okay.
You should go to the doctor. Numbness is a sign that there may be tendon or nerve damage. You may have compressed the nerve, swelling from the injury could be putting pressure on it, but it needs to be diagnosed by a professional. Failure to take care of this injury could lead to permanent loss or damage.
Yes, It's necessary. You should consult a doctor because many sentient nerves are located at finger tips so if it's numb it may lead to reduced blood supply.
