See this situation can be intermediating but its not impossible. Let me assure you if you are hardworking and if you have the perseverance and sincerity then you will definitely crack it.

Now the most important for NEET is that you need to focus on 10+2 as well as NEET. Thus you have to cover up both the portions simultaneously. Suppose the tution teachers or your school teachers will be teaching you the 10+2 syllabus, go through it in such that you prepare the syllabus of NEET as well as 10+2. This way at the end you will finish both the 10+2 syllabus as well as NEET 10+2 part. Now for the part of 11 you have invest some time every day to clear your backlogs. If you can study in bits both the 11 and 12 syllabus then by January you will complete 100% of 10+2 and NEET 10+2 part and 90% of the NEET class 11 part. Now depending on your preparation you can invest more time to class 11 and try on practicing problems which will really help you to have a great preparation.

Now you have mentioned that you are a HSC board student and you have to read NEET as well. Now the point is I don't think there will be a lot of deviation between HSC books and the NCERTs. So you can do a thing. Study from any of the book for the first and while revising you go through another books. For example you study Biology from NCERT then while revising go through the HSC book. This will help you to gather missing information if any and will assist you to score good in 10+2.

Also preparation can be really easy if you have good guidance. So having a good teacher or a institution can be really helpful. Career360 offers some really good courses for NEET as well as crash courses. So to stay tuned use the career360 app about the courses offered for 2022.

To know about career360 courses visit the link below:

https://learn.careers360.com/neet-coaching/?product=50&icn=NEET_knockout&ici=c360_sticky_qna_medical

To know about the study plan for NEET visit the link below:

https://medicine.careers360.com/articles/neet-study-plan

Also you should try to maintain a Summary Notebook in which you will write the important concepts and formulae which can be really helpful in the time of revision.

I hope this answer helps. All the very best for your future endeavors!