Are the black dots on my nose all blackheads?

No. Some are sebaceous filaments, normal structures that help move oil through pores. Trying to make every pore look empty up close can turn a normal structure into an irritation cycle.

Some nose dots are normal sebaceous filaments

They can become visible again after squeezing because they are part of how the skin functions. Blackheads are a different form of pore blockage. Repeatedly trying to empty every pore can leave irritation and marks, so focus on identifying the concern first.