I had covid starting this past june 22 for a week. i am a teacher and want to get my fourth booster vaccine before school starts in sept but its advised to wait 3 months after infection. can i get it after only 2 months because school is starting?

If the second booster (#4 shot) is required by your school, you can have it done; otherwise you do not need any more booster because it can't prevent another infection with a new variant. If you prefer to be vaccinated, you should wait for the new vaccines from Pfizer or Moderna which may have effect with omicron variants.

You misunderstood something you read. Covid immunization can be given within a week or two of recovering from covid.