How Long Does Tip Swelling and Hardness Last?

Tip swelling is an extremely normal part of the healing process after nose surgery. Nevertheless, the level of swelling present in a patient is a very individual thing and therefore it can not be determined exactly how long it will take for the swelling to go away completely.
I think you also needen't worry about the hardness of the tip that's present at the moment since it pretty much sounds like it is due to swelling.
It usually takes from 6 months up to a year for all the swelling to subside and the tip, in the majority of cases, is the last one to see the swelling completely resolve. 
At this point, you will just have to be patient! 
Good luck! 

Various factors contribute to swelling after rhinoplasty. Surgical delicacy, lifestyle, allergens, smoking, taping, nasal skin thickness and caring all contribute to the extent of postoperative swelling. A nose job shows its final result in 1 year. It sometimes even takes up to 2 years for some patients for their nose to have its final shape post surgery. Typically, you get operated, have your cast removed in 5-7 days and will have your nose swelling start to decline with time. I generally tell my patients that 70% of  swelling will be gone in 1 month, 90% in 3-6 months, 99% in 1 year and 100% in 2 years. 
The thicker your nasal skin, the longer your swelling takes to go away and hence the longer your recovery period. The thinner your skin is, the shorter this period will be and the quicker you will see your final results. Although the surgery is nothing the patient can control (other than choosing the right surgeon), other factors can be controlled. To prevent excessive swelling and promote healing, one should avoid smoking, avoid trauma, try to be away from allergens and use long-term tapings with proper massage (under control of his/her surgeon) to control edema and enhance the healing process. 
Hope this helps,Ali Rıza Öreroğlu, MD FEBOPRASEuropean and Turkish Board Certified Aesthetic, Plastic and Reconstructive SurgeonIstanbul, Turkey

this is difficult to answer without seeing pre op and current photos for comparison but 3-4 months is very early and especially if you had thicker skin you Rhinoplasty will be in it “infancy “ in terms of evolution Swelling will continue to settle over 12-14 months but if structural grafting has been used ( most modern rhinoplasties) then the firmness will remain long term which is a good thing and not a bad thing