No, you will not be able to continue using your card for transactions at the existing interest rate for the entire 45-day period. The existing rate will apply to transactions that occur 14 days or less from the date the credit union provided you the notice. After 14 days, the new interest rate will apply to further transactions. At the end of the 45-day period, the credit union can begin charging the new interest rate for any balances you incurred after the 14th day.
Please note that if your interest rate is increasing because you were more than 60 days late in making a required payment, the credit union can apply the new rate to all your balances.
If you wish to avoid the interest rate increase, you should consider contacting the credit union to close your account or not using your card for further transactions.