allowances are cumulative by month, so when she puts your code on and does your pay this month you get 3/12 of your allowance against your pay to date for this tax year. The total tax to date is then calculated and the tax paid to date is taken off. You then pay (or are refunded) the difference.
No need to reclaim from HMRC & should all be sorted this month.
BUT you may have missed the deadline for the June payroll, so might not be sorted until next month.