Convert JPG to PNG
PNG is the right choice when the file will be edited again, pasted into a document, or annotated — every save after this one is lossless. It will usually be larger than the JPG, because it is no longer throwing detail away.
Questions
Will converting to PNG make my image look better?
No. The detail a JPG already discarded cannot be recovered — PNG only guarantees that nothing MORE is lost from here on. It is worth doing before editing, not as a repair.
Why is the PNG bigger than the JPG?
PNG is lossless, so it stores every pixel exactly. For pictures that is usually several times the size of the JPG. Image KB Reducer runs oxipng over the result to make it as small as lossless allows.