It is possible. I would recommend you make a claim and even maybe talk to the business manager. If you cannot come to an agreement then, in Texas, you can sue for up to $10,000.00 in damages in Justice Court without the need of having to hire an attorney. Alternatively you can always consult with an attorney about pursuing a potential claim pursuant to the Deceptive Trade Act.
Maybe. As a general rule, when someone causes an injury/harm to you they are responsible for putting you in the position you were in prior to the loss. In other words, they must "make you whole." The real question is whether the damages you sustained for lost wages were reasonably foreseeable. In other words, by negligently changing the fuel filter, could the mechanic have reasonably foreseen that it may cause you to miss the freight load? Since you used the truck for your business, it appears to have been reasonably foreseeable you may have missed a job due to the mechanic's negligence. This assumes the truck had markings of a work vehicle and the mechanic knew it was a work vehicle.
As Mr. Wooten pointed out, you can file suit in small claims court for up to $10,000. Prior to filing any suit, I would contact the insurance company of the oil change business and try to negotiate your claim. If they are not willing to recognize your lost wage claim, then you may want to consider hiring a lawyer to pursue your claim. Keep all documentation you have concerning every aspect of the claim. Any documented admission you have from the company will be extremely important if the claim ends up in litigation.