My first instinct was that someone broke off the valve when pumping it up, but since you feel some pressure, that's ruled out.
Likely this is one of those foam filled tires that get introduced as the latest and greatest every few years. You'll know for sure if you remove the tire and the tube feels like Italian sausage. If you can get it apart, you can replace the tube and be good to go, but know in advance that it's really hard removing these types of tires.
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