Lagging happens now and then, but it sounds like you have had bad luck.
There are two things that will help you:
1. To get out of rookie. Can be done either through racing or time trialling. Also, SR can actually be gained through qualifying sessions, but you need to complete 4 races or 4 time trials anyhow. And only requirement for improving SR is avoiding incidents - you can go as slow as you like.
2. Improve your iRating. At the moment you can't see it, but it is there. And, in fact, you can find it if you look at your latest result and click "Output CSV". iRating is the basis for the splits - generally the higher up, the better the racing. As a general rule, not a guarantee. Note that even if you get promoted to higher classes, you will most likely still run into bad driving in the lower splits.
So, besides that, practicing before racing will be a good idea. If you are well prepared, you will avoid making mistakes on your own, which naturally helps SR, and also you will profit from your gained consistency when others screw up. And in rookie, they often do
Also, during a race, there are things you can do. If you identify the moron of the field before he hits you, you have the option of letting him go when he gets close. There's a chance he will screw up later, possibly even taking others with him, gaining you a few positions. At least, by letting him go you will lose only one position instead of various, and your SR will be grateful.
Furthermore, to minimize chances of being rear ended, you can choose defensive lines approaching corners. If the driver behind is not directly behind, there's less chance he will bang right into you. Also, if you go towards the inside before braking, he will (most likely) not try dive bombing on the inside, thus you will remove the possibility of being pushed wide. Your speed will suffer, though, keep that in mind.
Particularly for cars with brake lights it may also be a good idea to brake rather lightly at first, to light up the brake lights. This will in most cases be a good clue for the following driver to start braking, so when you a short moment later apply full braking power, you have a better chance of surviving.
EDIT: Also, get to know the spectate function. It could be a good idea to spectate a few races (you can drive as a ghost) and get to see how people drive in both upper and middle splits.