How do I pursue a skincare company if its product scarred my face?

You can sue them for your medical costs and--if there will be lasting scarring or disfigurement--potentially some amount of "pain and suffering" (in an amount commensurate with the level of scarring) IF you can show, with scientific evidence (e.g. with tests of the product, which you'd have to pay for) one or more of the following:
1) That the product was improperly formulated--that is, its formula or what it is made of had a reasonable potential to harm the average person; 
2) That the product was improperly manufactured--that even if safe if made correctly, in some way, this batch was not made right or was adulterated; 
3) Risks or side effects were not adequately disclosed; and/or
4) The instructions for safe use were not adequate.
So you have to show that the company did something wrong in some way; and if you can, you can potentially recover compensation, though you have to balance the amount you could recover (based on your medical costs and degreee and permanance of scarring) vs. the cost of the lawsuit (e.g. testing the lotion; having a scientific expert write a report and testify, if needed; legal fees, if you hire a lawyer; etc.) to see if it is worthwhile doing.
On the other hand, if the lotion was safely formulated and manufactured, any disclosures of risks was adequate, and the use instructions were sufficent, and the problem is that you misused it (e.g. left it on too long; or used it when you should not have [e.g. when on some medication which you should be on when using a product like this]) or are simply unusually sensitive to it, they would not be liable. They are not liable simply because you were hurt; you have to establish some wrongdoing on their part for liability.