Hello student, 
With a score of 556, as you are from general category, you have chances of procuring a seat in the government medical colleges like Jawaharlal Nehru Medical College, Bhagalpur, Vardhman Institute of Medical Sciences, Nalanda, Anugrah Narayan Magadh Medical College, Gaya etc. when comparing the results of previous years.  But, one thing to keep in mind is that scores and ranks vary each year with difficulty level of the question paper and availability of seats. However, you can visit the link below to check the previous year cut-offs of Bihar: https://medicine.careers360.com/articles/neet-cutoff-bihar

• Anugrah Narayan Magadh Medical College and Hospital, Gaya
• Darbhanga Medical College, Laheriasarai
• Government Medical College, Bettiah
• Indira Gandhi Institute of Medical Sciences, Sheikhpura, Patna