Hello and welcome. I'm Dr Chip.
This sounds more like an infected sebaceous cyst although the spot on your nose could be acne.
You can try washing your face with Betadine cleanser and then applying topical Neosporin ointment to see if these will clear up, but, if that doesn't help, you'll need prescription oral Doxycycline antibiotic for this.
Please let me know if you need any more information.