My nose is filled with blackheads. What should I do? Squeeze them out or leave them be?

Don't squeeze. If you squeeze them you may cause an infection. It is better to get a professional facial treatment with steam and extraction, followed by some therapeutic lotion to help open your pores.
Leave them. Do not pick at blackheads. You could cause a skin infection leading possibly to whiteheads (pus-filled). More importantly, it increases the chance of scarring. Use an acne medication (creams, solutions, pills) as recommended by your primary care doctor or dermatologist.