Generally you get one carry-on - like a small suitcase - and one personal item, like a purse or a computer case. The carry-on has to be within the allowed dimensions of the airline - for example Delta's is 56 x 36 x 23 cm. If the pillow is no more than that size, you can bring it.

Yes, you are absolutely allowed to bring a pillow on a Delta Air Lines flight, and it usually does not even count toward your carry-on or personal item limit. Most airlines, including Delta, consider a standard neck pillow or a small travel pillow to be an "exempt item" or a "personal accessory" that you can carry in your hand or wear around your neck while boarding. If you choose to bring a full-sized bed pillow from home, it is generally also allowed, though you should be mindful of its size; if it is exceptionally large and takes up significant space in the overhead bin, a gate agent might ask you to tuck it into your suitcase. Bringing your own pillow is a popular choice for Delta’s "red-eye" or long-haul international flights to ensure comfort, as the complimentary pillows provided in Main Cabin are often small and thin. If you are flying in a premium cabin like Delta One, a high-quality pillow and duvet are provided at your seat, but you are still welcome to bring your own for personal preference. Just ensure your pillow is clean and doesn't have any loose fillings that could create a mess in the cabin.