Hello,

You are eligibile to appear for NEET 2019 exam, considering you fulfill the eligibility criteria. Why are you fearing for the rule? Nothing can be said or assumed now about the rule for number of attempts. 
If the authorities limit the number of attempts to three times then also you will have two more attempts. So, if you wish you can appear for the NEET 2019 exam.

Also, NEET is the largest entrance exam for admission to medical, dental and AYUSH courses. If you are appearing, you should prepare well for the exam. Application forms of NEET 2019 are available till November 30, 2018.
Good Luck!