Get rid of automatic double angle brackets in text box

It sounds like a bullet or paragraph style is being applied by default.

In InDesign, whatever formatting is active with the Text tool becomes the default for new text frames.

Try this

Make sure nothing is selected on the page (click on the pasteboard).

Select the Type tool.

In the Paragraph panel, turn Bullets off (and check numbering too).

Open the Paragraph Styles panel and make sure you’re not automatically typing into a style that includes those double angle brackets.

Once you clear the formatting with nothing selected, it should stop inserting them automatically.