Detected fraudulent charges to my account but I cannot close the card until another payment goes through

Today I detected two charges to my card, both on the same day. I called my bank (chase) but the only solution offered was to block and close the card. However, I am currently doing some processes with USCIS and until they charge the fee attached to my paperwork I cannot close the card since then that process would just fail.

If the process fails, my process would be rejected and it seems I cannot resubmit the process per https://www.uscis.gov/forms/pay-a-credit-card:

You may use Visa, MasterCard, American Express, and Discover. Make sure the card has enough money to cover the fee. We will reject your application, petition, or request if the card is declined, and we will not attempt to process your credit card payment a second time.

This is a special circumstance where a payment must go through on the potentially compromised card.

Does anyone know any other option to ensure that that payment goes through but also preventing further charges in a card that might have been compromised? Are charges like that usually because of a compromised card? Or some kind of sweep/random scam?