You are spot on for your goals. Unfortunately, there is no magic answer to this. You should contact a Memphis attorney who understands how to deal with traffic violations, as the attorney should have some ideas for coming up with defenses. Typically, fees to retain an attorney are lower than the financial consequences of having these tickets on your record not to mention the potentially negative effects on your privilege to drive.
This answer is given merely for informational purposes and does not create an attorney-client relationship. For specific advice, contact an attorney in your state to see if working together makes sense.
Sometimes driving school is an available alternative to having to pay a fine on a speeding ticket. By contacting the local traffic court clerk, you may be able to find out more details about this alternative. Often, if a person is allowed to complete driving school, the court would dismiss the traffic ticket and you would not receive any "points" on your record for that particular ticket. However, it may complicate things that you received two tickets in quick succession. A local attorney should be able to advise you in more detail as to the available possibilities in your case.
I would be happy to discuss these tickets with you. Feel free to contact me at my office. (901) 529-8500. It is likely that we can get the first ticket dismissed which should help when dealing with the second ticket. You likely will come out better in traffic court with a lawyer than without one.