Is it possible to lengthen the nose?

Yes. This is a common part of non-Caucasian rhinoplasty. I would highly recommend seeing a board eligible or board certified plastic surgeon for a physical exam and accurate analysis with safe recommendations for potential surgical options. Best of luck!

Lengthening the nose is extremely difficult to achieve. It typically would require cartilage grafting and even so the amount of lengthening would be minimal

Lengthening a short nose: lengthening a short nose can be a disappointing undertaking. It can be done by harvesting a rather large piece of cartilage from the septum and adding it to the caudal septum as a septal extension graft. It usually however only achieves a small amount of lengthening, which is why I say it can be disappointing.