Converting PNG to EPS

[Maggie2503117964wj]

Hi everyone, I am trying to convert a bunch of PNG logos for a school into EPS files. The school's logo has a heavy white stroke around the logo and every time I do image trace>expand>ungroup, the white stroke ends up being selected to the background and then I am only left with the red words without the white stroke around them... 

If anyone has a better idea of how to convert this type of logo to an EPS without losing the white stroke/outline I am all ears. 

[Ton Frederiks]

You could make the canvas size a little larger in Photoshop and add a black background.

Image Trace, expand and delete the black.

[Met1]

Just reset in Illy. It's only type: Rockwell?

[Maggie2503117964wj]

Yep it is Rockwell

[Ton Frederiks]

That is what I thought at first, but Rockwell looks different.

[Maggie2503117964wj]

I just started here so I'm not 100% sure tbh