Amanda Bynes -- Signs of Schizophrenia

Amanda Bynes is exhibiting signs of schizophrenia ... and medical professionals and others WILL seek a 2-week extension on her 5150 psychiatric hold so doctors can properly diagnose her ... sources familiar with the situation tell TMZ.

We're told ... ever since Amanda was taken into custody Monday night -- after she lit a fire on an elderly woman's driveway in Thousand Oaks, CA -- people close to Bynes are convinced she's suffering from mental illness, specifically schizophrenia.

Sources tell us ... Amanda's parents will now ask a judge to put the 27-year-old in a conservatorship, a la Britney Spears, because they believe she is unable to care for herself and could be a danger to others.

Amanda's parents have wanted to take action for the past couple of months -- but they didn't have the goods because Amanda's conduct was not so over the line that a judge would take away her freedom.

Now, after the driveway fire incident ... the circumstances may have changed enough to convince a judge Amanda needs help and supervision.