What converting to PNG can and can't do
PNG stores pixels losslessly, so the PNG is an exact copy of how the JPG looks. Editing and re-saving it won't add new compression artifacts the way repeatedly saving a JPG does.
Converting cannot restore detail that JPEG compression already discarded. Blockiness or soft edges in the JPG will be preserved faithfully in the PNG. And a converted photo won't gain a transparent background — the background is part of the image.
Expect a larger file
JPEG achieves small sizes by discarding detail; PNG keeps every pixel. A PNG copy of a photo is typically several times larger than the JPG. That's normal. If you want a smaller file, keep the JPG or use Compress Image.