Hello,
With your score you have few chances of getting into government medical colleges of your state  as usually cutoff was 415+ for in himachal pradesh under 85% quota.

You can still get into the following medical colleges at himachal pradesh:-

Dr. Yashwant Singh Parmar Government Medical College, Nahan, Sirmour

Pt. Jawahar Lal Nehru Government Medical College, Chamba

Shri Lal Bahadur Shastri Government Medical College, Mandi

With 420 NEET score your Overall Percentile will be around 92.21 - 92.91  and your NEET AIR Rank will be around 71349 - 68499

However these information is based on last years cutoff and as cutoff changes every year depending on factors like difficulty and number of candidates and recent COVID19 situation etc.

You can use careers360 college predictor to know the colleges you can get at your NEET score;-

With a score of 421, your rank might be approximately between 99914-109429 . This is an expected rank range: https://medicine.careers360.com/articles/neet-result-marks-vs-rank . Now regarding the Colleges that you may have a shot at, in 2017, under State Quota 395 marks secured a seat in Pt. Jawahar Lal Nehru Government Medical College. That was ST cut off. We do not have 2019 data but with 421 marks, your have borderline chances.

Having said that, this is based on 2017 data and cut offs change every year. Cut offs change every year depending on various factors such as no.of Candidates appearing for the exam, no.of Candidates qualified, top NEET score and difficulty of the exam. For a complete list of colleges that you may have a shot at, please use our College predictor: https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer