Missing person question

Question y’all. I called Harris County’s non-emergency line to report that my sister was missing but last heard from on Friday around midnight, calling from Fry/Park Row. They were supposed to send an officer to me to file a police report. Fair enough. So, then a lady called me and asked me a few more questions. She said she was not in their system but could see something about her resisting an officer on that same Friday. But she said it had to be out of their agency because she couldn’t see anything else about it. From Harris, Fort Bend, Waller, Brazoria, etc ( basically ever adjacent county), she is not in a jail. No new charges. She was released from jail at random (wasn’t supposed to be released until September) and was supposed to take the bus to a rehab in Austin, but because she’s off her rocker, she came straight to Houston with no where really to go, no ID, no phone, etc. She was calling from random businesses and strangers phones for the first few days. As far as we can tell she’s not in any of the psych wards. In this number of days, she would have called. Even if she was in the psych ward (not her first time if that’s the case), she would have called. It’s like she vanished. Ideas on where to search (which agency)?

She’s about 5’8, 120lbs, white with dark hair and blue eyes, and has very severe mental illness.