Have I Damaged my Nose Permanently by Squeezing Blackheads?

Manipulation of the skin following rhinoplasty surgery is unlikely to cause structural damage to the underlying bone and nasal cartilage.  However, squeezing blackheads might cause damage to the skin itself.  It’s important to realize that the skin has compromised blood supply in the immediate post-operative period.  For this reason scarring, skin necrosis and prolonged swelling could result from this type of maneuver.
            Under these circumstances, it’s reasonable to avoid this type of activity in the future.  Since you don’t have skin damage at this time you’ll probably be okay going forward.  If you still have concerns it’s important to consult your surgeon.  Your surgeon should be able to address your concerns and alleviate your anxiety.

I understand that the sudden appearance of some swelling after you squeezed the skin of your recently operated nose might have given you a fright, but it is not very likely you did any permanent damage to the underlying structures. 
Nevertheless, you should avoid any rough contact with your nose and keep it as far away from every possible trauma to ultimately avoid really jeopardizing the results that you're satisfied with.
If the swelling doesn't subside in a week or so, you should definitely consider consulting with your surgeon, who will surely know how to proceed accordingly.

It would be VERY unlikely that you damaged anything. The swelling will subside with time, and it's common for the nose to be susceptible to swelling after rhinoplasty.