Don't do it with SQLite.
Do it with your programming language, your framework that is using SQLite.
In the table, where you have the column with the html code, add additional columns for data about the html. You will have to gather the data for the extra columns, while you analyze the html with your framework.
Track data about the structure the html format does have and save in an extra column the textual content of the html data.
You can get all tags by simple REGEX:
/<?[^<>]+>?/
Checkout how you receive data by scanning the html data for tags with the regexp above and write an iterated evaluation for tag-content (i.e. if a string in the results-array starts with a "<" it´s a tag, by scanning it with /<\s*\/\s*[^>]+>/
you will see if it is a ending tag and by scanning it with /<\s*[^\/>]+\s*\/\s*>/
you will see if it is a single closed tag. If none of the differentiated states does apply, it is textual content.