JSFiddle - React, Tailwind, and code Playground

JavaScript

const isMoreThan3MonthsHence = ({ utcYear, utcMonth }, 
                                now = new Date, 
                                target = new Date(Date.UTC(utcYear, utcMonth)), 
                                threeMonthsAway = new Date(now.valueOf()).setUTCMonth(now.getUTCMonth() + 3)) => 
    (target > threeMonthsAway)


console.log(isMoreThan3MonthsHence({ utcYear: 2020, utcMonth: 7 })) // true (correct!)

const validate = (str, 
                  [month, year] = str.split('/'), 
                  date = new Date(Date.UTC(+year, (+month)-1))) => 
    isMoreThan3MonthsHence({ utcYear: date.getUTCFullYear(), utcMonth: date.getUTCMonth() })

// Note: input is one-based months
console.log(validate('07/2020')) // Now true