Plenty of good stories here of people coming back with no problems. Make sure you can get a doctor's note from your home country stating your dad's issues.

There's always a small risk and that's stated on your AP letter once you receive it but many stories written here with a good ending.

Also, if you came with no visa, the AP will enable you to change your status faster and easier. Do a search on this forum and you will find out plenty of similar stories. Research before you do anything.