Yes you will have to go for the private colleges only as you vae scored very less marks in NEET. In physiotherapy there is no such bounding criteria like MBBS and Dental courses as the admissions will be based on the merit rank and the marks in entrance you have obtained. For the BAMS courses all you have to go for the counselling rounds conducted by the state admission committee and based on your merit rank you will be able to get the seat. The link for the BAMS colleges in mumbai is provided where you can find out the list of various BAMS colleges and their fees.

https://medicine.careers360.com/colleges/list-of-bams-bachelor-of-ayurveda-medicine-and-surgery-colleges-in-maharashtra

Also the link for the physiotherapy colleges is also provided.

https://medicine.careers360.com/colleges/list-of-physiotherapy-colleges-in-mumbai