I know nothing about the type of car you are running or anything about front wheel drive but let me at least help you think about this
First- some tire spin is good. No car goes down the track without some give some where. slippage occurs through tire spin, clutch, transmissions, and convertors. You do not want your car to lock up 100% in 2nd gear
On our ProMod car, we control tire spin by adding or taking away power during certain points in the run, or by adjusting the amount of slippage that occurs at a given point. If you are spinning your tires in 2nd gear and it is causing you to lose time, you are putting to much power to the ground at that point based on your current set up. It means that the wheel speed of your tire is too high to grip the surface of the track. So you must think about how you can soften 2nd gear or slow the tire down- in other words improve the tires ability to grip the track surface. One thing to try is to lower your 1st and/or 2nd gear shift RPM- thus taking power away and reducing the wheel speed that leads to tire spin.
You may want to consider what electronic control devices are available for your car. Certain devices are made to help control traction problems and some devices will allow you to control your tune up. For example, Taking timing out at a given point will also lower wheel speed by taking power away
If you have an adjustable clutch, it may not have enough slip at 2nd gear meaning it is locking up too much and spiining the tire too fast.
A new tire does not mean you are running the right tire. It may be time to start asking questions about various types of racing tires that are better at gripping the tracks surface
Remember that your tire spin condition will change depending on both the track surface and temperature.
New racers sometimes think that putting a big horse power engine in a car will make them go faster. Racers who are experienced start to think about how they are going to get their power to the ground and use it in the most effective manner.
I hope I have not been too overly simple, but you did say you were new. I hope this will help you think about your problem in a new way