hello,

I HOPE YOU ARE DOING FINE.

Yes you can become a doctor without clearing NEET, the only disadvantage being that you cannot study MBBS in India. There are lot of countries that offer MBBS seats without the condition of clearing NEET. There are several countries that offer medical degree at much lower cost than India.But, the quality of education is a question mark.
If you want to work as a doctor in India after finishing your medical graduation in some other country, you will have to clear the MCI entrance exam. That again do not make a huge difference because even Indian students have to take up the exam from this year onwards.

ALL THE BEST.