Can I sue them for everything they got for trying to cover the accident up and medical bills?

I do not know what everything they got equates to in dollars and cents. That said, the fact that you have pictures is your evidence of the negligence. You can go ahead and sue them using your pictures as evidence that they created a dangerous condition. I would sue the apartment owners and the individual who actually created the oil puddle that you fell in. Also, if you have the clothes you were wearing at the time of your fall, keep them, as they, too, are part of your evidence of the substance that you slipped on.

If you can prove that is what occurred, i.e. that they negligently let the water, soap and oil pile up without posting warnings about it, and that caused you to fall, you would be entitled to make a claim for your medical bills and pain and suffering.

If you have photos of the dangerous condition, you have some proof of what caused your injury. Go see a personal injury attorney with all your evidence and medical bills and I'm sure he or she will say that your evidence can be helpful to you in establishing your case. If the defendants deny creating the dangerous condition, your photos will make them look like liars, and neither judges nor juries like liars at trial. Good luck to you.

Yes, you can sue; anyone can sue anyone. The real question is whether or not you'll be successful. By their nature, slip and fall cases are problematic, but if your injuries are substantial I'm sure you can find an attorney who will be interested in helping you.

Yes based on the limited facts that you have provided, you can very likely pursue a claim against their insurance company for your medical bills and pain and suffering.