Dúvida Tomcat e Mysql

Pessoal, preciso muito de ajuda, pois agora buguei o cérebro...

Eu tenho este código pra abrir uma conexão no mysql

package br.com.rlbc.DAO;

import java.sql.DriverManager;
import java.sql.SQLException;

import com.mysql.jdbc.Connection;

public class DataBase {

    private String url;
    private String user;
    private String password;

    public DataBase() {
        url = "jdbc:mysql://rocket-league.mysql.uhserver.com/rocket_league";
        user = ""; //removido apenas aqui no alura
        password = ""; //removido apenas aqui no alura
    }

    public Connection getConnection() {
        Connection connection = null;
        try {
            connection = (Connection) DriverManager.getConnection(url, user, password);
        } catch (SQLException e) {
            e.printStackTrace();
        }
        return connection;
    }
}

E tenho esta classe para consulta

package br.com.rlbc;

import java.sql.PreparedStatement;
import java.sql.ResultSet;
import java.sql.SQLException;
import java.util.LinkedList;

import com.mysql.jdbc.Connection;

import br.com.rlbc.DAO.DataBase;
import br.com.rlbc.redirects.Time;

public class CampeonatosDAO {

    private Connection con;

    public CampeonatosDAO() {
        this.con = new DataBase().getConnection();
    }

    public LinkedList<Time> getTimes(String campName) {
        String sql = "Select * from CAMPEONATOS where campeonato = ?";
        try (PreparedStatement stmt = con.prepareStatement(sql)) {
            stmt.setString(1, campName);
            stmt.execute();
            try (ResultSet resultSet = stmt.getResultSet()) {
                LinkedList<Time> times = new LinkedList<>();
                while (resultSet.next()) {
                    times.add(new Time(resultSet.getString("time")));
                }
                return times;
            }
        } catch (SQLException e) {
            e.printStackTrace();
        }
        return null;
    }
}

Eu criei esta classe de teste que funciona normalmente...

package br.com.rlbc;

import java.util.LinkedList;

import br.com.rlbc.redirects.Time;

public class TestaCampeonato {

    public static void main(String[] args) {
        LinkedList<Time> times = new CampeonatosDAO().getTimes("2v2free");
        for (Time time : times) {
            System.out.println(time);
        }
    }

}

Mas quando eu tento acessar através da URI

package br.com.rlbc.redirects;

import java.io.IOException;
import java.util.LinkedList;

import javax.servlet.RequestDispatcher;
import javax.servlet.ServletException;
import javax.servlet.annotation.WebServlet;
import javax.servlet.http.HttpServlet;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;

import br.com.rlbc.CampeonatosDAO;

@WebServlet(urlPatterns="/informacoes")
public class Informacoes extends HttpServlet{

    private static final long serialVersionUID = 1L;

    @Override
    protected void doGet(HttpServletRequest req, HttpServletResponse resp) throws ServletException, IOException {
        String parameter = req.getParameter("camp");
        RequestDispatcher dispatcher = null;

        if (parameter.equals("2v2premium")) {
            dispatcher = req.getRequestDispatcher("/WEB-INF/jsp/2v2premium.jsp");
        } else if (parameter.equals("2v2free")) {
            LinkedList<Time> times = new CampeonatosDAO().getTimes("2v2free");
            dispatcher = req.getRequestDispatcher("/WEB-INF/jsp/2v2free.jsp");
        } else if (parameter.equals("2v2chave")) {
            dispatcher = req.getRequestDispatcher("/WEB-INF/jsp/2v2chave.jsp");
        }
        dispatcher.forward(req, resp);
    }
}

Encontro o seguinte problema:

java.sql.SQLException: No suitable driver found for jdbc:mysql://rocket-league.mysql.uhserver.com/rocket_league
    at java.sql.DriverManager.getConnection(DriverManager.java:689)
    at java.sql.DriverManager.getConnection(DriverManager.java:247)
    at br.com.rlbc.DAO.DataBase.getConnection(DataBase.java:23)
    at br.com.rlbc.CampeonatosDAO.<init>(CampeonatosDAO.java:18)
    at br.com.rlbc.redirects.Informacoes.doGet(Informacoes.java:28)
    at javax.servlet.http.HttpServlet.service(HttpServlet.java:624)
    at javax.servlet.http.HttpServlet.service(HttpServlet.java:731)
    at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:303)
    at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
    at org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:52)
    at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241)
    at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
    at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:218)
    at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:122)
    at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:505)
    at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:169)
    at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:103)
    at org.apache.catalina.valves.AccessLogValve.invoke(AccessLogValve.java:956)
    at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:116)
    at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:442)
    at org.apache.coyote.http11.AbstractHttp11Processor.process(AbstractHttp11Processor.java:1082)
    at org.apache.coyote.AbstractProtocol$AbstractConnectionHandler.process(AbstractProtocol.java:623)
    at org.apache.tomcat.util.net.JIoEndpoint$SocketProcessor.run(JIoEndpoint.java:316)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1142)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:617)
    at org.apache.tomcat.util.threads.TaskThread$WrappingRunnable.run(TaskThread.java:61)
    at java.lang.Thread.run(Thread.java:745)
set 25, 2016 3:55:39 PM org.apache.catalina.core.StandardWrapperValve invoke
GRAVE: Servlet.service() for servlet [br.com.rlbc.redirects.Informacoes] in context with path [] threw exception