It sounds like you have a stroke set on your text. There are couple of ways to fix this.
Make sure the text box is selected, then open the Fill and Stroke Panel using Ctrl+Shift+F. This is where you can delete or change strokes and fills. Select the Stroke Paint tab. The X button on the left will delete the stroke completely. Similarly to change the fill, go into the fill tab.
You can also fix the problem with the Text Tool acting in unexpected ways. If you go into Edit > Preferences > Tools > Text, you can set the Style of New Objects setting to This tools own Style. This will mean the default will always be the same, so even if you set a stroke, the tool will return to its default next time you use it.
If the option in there has a stroke set, you can select some text that has no stroke and hit the button that says "Take from Selection". That will store it as the default.