I was recently sworn in as a US citizen, can I travel on my still valid non-US passport before I actually apply for a US Passport?
If you are a frequent traveler and were recently sworn in as a US citizen, you will have had to surrender your I-551 (Green Card) at the swearing in ceremony. This document would normally serve as your proof of your right to legally reside in the United States upon your return to the US, should you travel on the non US passport.
The problem this will pose, however, would be on your return to the USA. All US citizens MUST be in possession of a valid US Passport in order to return and gain reentry back into the USA via air from a foreign country. Persons returning to the US on a non US Passport must be in possession of valid passport along with a valid US visa, Green Card or an ESTA (being a national of one of the US Visa Waiver program countries for which the limit of stay in the would be only 90 days).
USCIS (US Citizenship and Immigration Services) strongly recommends allowing sufficient time between your naturalization ceremony and any planned travel to receive your US Passport. Currently as of this writing, routine service for a US Passport can run up to 18 weeks, due to the pandemic.
Expedited service is available through Peninsula Visa.
Please visit https://www.peninsulavisa.com/passport-services for complete details and instruction.