Look closely at your loan doc’s to determine conditions under which PMI might be removed. In many cases it cannot be removed within a year or two of origination, regardless of value.
The best time to get an appraisal is shortly after a nearby similar house is sold at a higher price.
I think it is highly unlikely that your lender would accept an appraisal within a month or two of your purchase over the original appraisal. (Did it happen to appraise above/below the price you paid?)
