HI Justin,
One key factor is how long ago you received those tickets and what they are for. Generally after three years, traffic infractions like speeding tickets will be removed from your record, putting you in a much better position to obtain insurance.
Honestly, you will not find good rates, as you have three strikes against you at the moment:
-multiple citations,
-under age 25, and
-male
Driving without insurance is simply not a viable option either. It is not only against the law, but it could easily jeopardize your financial future should you be involved in an accident.
Insurance companies don't like to advertise this, but they generally insure the car, and not the driver. That means if you used a friend or parent's car for critical trips, you would be covered (as long as you remain a legal driver).
Given that, I would counsel you to swallow hard, sell the car, and bank the huge insurance premium you won't have to pay. Then give generous gas & maintenance money to family members and friends who are willing to loan you their vehicles. Then don't get any more tickets!
Once your tickets "age off" your account, your rates will come down substantially, especially if you can qualify for other discounts (like "good student" designation). At that time, owning a car will be a more affordable proposition for you.