Detect Magic will not identify a polymorphed Changeling.
Only spells (or abilities that replicate specific spell effects or invoke a "spell attack"), magical items, and effects specifically clarified as being magical by descriptive text count as capital-M Magic, which would be detected by Detect Magic. Otherwise, even something which would seem supernatural to us is just part of the "background magic" of the world, which is a part of nature and always functions, and is not considered magical as far as game rules are concerned (as per Sage Advice).
The changeling's Shapechanger ability states:
Shapechanger. As an action, you can polymorph into any humanoid of your size that you have seen, or back into your true form. However, your equipment does not change with you. If you die, you revert to your natural appearance.
Contrast with, for instance, the Change Shape ability of certain dragons, which always has wording like:
Change Shape: The dragon magically polymorphs into a humanoid or beast that has a challenge rating no higher than its own, or back into its true form.
The dragon's ability is expressly magical. The Changeling's ability is not. Therefore, effects that detect magic are no use in identifying a polymorphed changeling, though they would help you spot a polymorphed dragon.
There are, however, other means to identify a polymorphed Changeling.
Any being with Truesight can:
see in normal and magical darkness, see invisible creatures and objects, automatically detect visual illusions and succeed on saving throws against them, and perceive the original form of a shapechanger or a creature that is transformed by magic
The most obvious way to gain Truesight is the use of the 6th-level spell True Seeing.
The spell Moonbeam also has an extra effect when it targets shapechangers, as failing to save against the spell forces them to resume their original form - though this is a damaging spell, so probably not one to use unless you're already on very bad terms with your suspected polymorphee.