You do not have to remove your own magic items for detect magic to work
When you cast detect magic (PHB, 231), the spell allows you to (my emphasis):
...sense the presence of magic within 30 feet of you. If you sense magic in this way, you can use your action to see a faint aura around any visible creature or object in the area that bears magic, and you learn its school of magic, if any.
Let's say that before you cast this spell you also have some other spell ongoing on your person, that you currently have 2 known items and 1 unknown item that you don't know if it's magic or not, and that there is an unknown magic item in the room within 30 feet of you.
Detect magic will first tell you there is magic within 30 feet of you.
You can stop there and be happy in the confirmation you have a known spell and some known magic items, or you can can use your action to see the aura around the individual items listed above, discover new auras, and learn the item's school of magic (if any).