I don't care if you don't beleive it to be true or not. But a fact is a fact. A set of wheels and tires that are lighter and of gripier compound respective than what your car came with stock will result in a faster car than what it was when it was stock, period. You do not have to spend 3k on a set of wheels and tires to result in a lighter weight setup than what your car came with. In fact, realistically, no matter what you spent on your wheels I bet they are lighter than what you had on your car before even if they are a full 2 inches larger in diameter. Your stock rims were, in all likely hood, made of steel. I don't know what kind of wheels you currently have on there but I bet they aren't made of steel. So the chances are good that they are lighter. BUT, since they have a larger diameter than their "rotational mass" (see previous post) has more leverage since it has a greater distance from center of the wheel to the outer edge. Therefore there is more momentum to move INITIALLY. This will result, "maybe", in a bit slower performance off the line than the 16's but since there is now more diameter and more momentum your car may achieve a faster top speed. Again proving that in some or all respects wheels may make your car faster. Also, if there is less rotational mass like mentioned above, the amount of pressure and friction required to stop your car may be less and therefore your car would also stop faster than stock. Unless ofcourse, like also explained above, there has been a change in the weight valuation because of the increased diameter and therefore it may take longer to stop than stock.
Tires, too simple, your stock tires (like everyone else's btw) were likely some crappy all season rubber with a very stiff compound. (this is not because I am saying your car is crap, it's not. but this is just the reality that most car companies don't put the most amazing tires on their cars) This is not conducive to maximim torisional or lateral grip. BUT, your sport tires are softer compound and would be more conducive to better lateral and torrisional grip. If I need to explain why grip is important to the "speed" of your car, you haven't learned much from your accident. Stopping, going forward and lateral movement are all elements which make a car faster.
You said you were turning and you didnt make the turn but instead you went straight. What your car did is called understeer. Your front end was "pushing" and so you're front wheels were slipping and they didnt have grip to change directions. One method of changing your cars direction when this is occuring is to stab the break quick, unweighting the rear end, and causing the car to "step out" or "oversteer". This is relevant because it may have helped you make the corner. It wouldn't have stopped you any faster. But it just might have got you around the corner. Give it a try in a parking lot somewhere and look up some tips online.
It's unnecessary for me to sit here and talk about my cars and how I paid for them or not. It's really quite irrelevant to the point I am making. Which btw, if it's not already apparent, is that adding neons is stupid. I am also atleast glad to hear that you paid for your car yourself and aren't bastardizing it with your parents money. But, since you did ask, and for the sake of proper argument I can show you my vehicles if you'd like. My picture hosting service is down right now, but i'll come back and post pictures when it's back up. If you would like to have a look for a similar vehicle, google 2004 VW R32 and 2005 GMC sierra quad cab duramax. I am 23, and ofcourse i paid for it myself. But since you are 17 I guess we can talk about my vehicle when I was that age. I bought at that time a new jetta 1.8t all options. Which BTW, is FWD and you can cause a FWD car to oversteer with the method above. All my own earned money ofcourse. But again, this is completely unneccessary to my original argument, but only because you asked.