Supposing you keep pushing on the tip of your nose really hard. will the cartilage break and will the tip be lifted a little?

NO - STOP!: If you are thinking of trying do-it-yourself Plastic Surgery on your nose, I strongly advise against it! Your current idea is much more likely to cause bleeding, pain, swelling, and deformity at the end or bridge of your nose, not the lift you are hoping for. Plastic Surgeons spend close to 20 years in college, medical school and residency training - don't ruin your face and spend $$ to fix it.