How can I add escape characters to a Java String?

I'm not claiming elegance here, but i think it does what you want it to do (please correct me if I'm mistaken):

public static void main(String[] args)
{
    String example = "Hello, I'm\" here";
    example = example.replaceAll("'", "\\\\'");
    example = example.replaceAll("\"", "\\\\\"");
    System.out.println(example);
}

outputs

Hello, I\'m\" here

For others who get here for a more general escaping solution, building on Apache Commons Text library you can build your own escaper. Have a look at StringEscapeUtils for examples:

import org.apache.commons.text.translate.AggregateTranslator;
import org.apache.commons.text.translate.CharSequenceTranslator;
import org.apache.commons.text.translate.LookupTranslator;

public class CustomEscaper {
    
    private static final CharSequenceTranslator ESCAPE_CUSTOM;
    
    static {
        final Map<CharSequence, CharSequence> escapeCustomMap = new HashMap<>();
                    
        escapeCustomMap.put("+" ,"\\+" ); 
        escapeCustomMap.put("-" ,"\\-" ); 
        ...
        escapeCustomMap.put("\\", "\\\\");
        ESCAPE_CUSTOM = new AggregateTranslator(new LookupTranslator(escapeCustomMap));
    }

    public static final String customEscape(final String input) {
        return ESCAPE_CUSTOM.translate(input);
    }
}