I was told by a realtor that the house automatically goes to me as the only child...
There is a kernel of truth there. If there is no surviving spouse, and you are the only issue, then the intestate succession statutes of Illinois would make you the only heir. And, if there are no creditors, then the property would pass to you. However, unless you were a co-owner with the right of survivorship, it isn't automatic.
...and the title company will allow me to sign as seller.
Well... I don't know about Illinois (especially Cook County, if that is where you are located), but, where I come from, unless you are the owner - meaning, like, having your name on the deed as the owner - or can produce those letters issued by the probate court that show that you are legally authorized to act on behalf of the estate, you are going to have problems. There's nothing like getting to closing and running into a big "Uh oh!".
Ask the realtor where he/she received his/her law degree.
Do a search on: Illinois probate
You can probably get a few 15 - 30 minute consults with probate attorneys without charge.