I think you would be in year 11, if you were 16 on the 3rd of September this year, so should be in the last year of GCSEs courses. Phone up (or ask a carer to phone) your local education authority and tell them your date of birth (to make sure you should be in year 11) and ask them to help you find a school. They should be able to tell you which local authority schools have places and how to apply. They should also be able to tell you about academies near you. These are state schools but they organise their own admissions and might not be able to give you a place.
If you don't know which is your local authority let us know roughly where you live (just the name of the town, no more details on -line) and someone may know who to contact.