In Texas if you are on the job and the employer does not subscribe to Texas Workers Compensation then you may very well have a compensable claim. You only have show negligence on the employer. I would definitely contact an attorney. There are statute of limitations on filing these claims, so I would do so sooner rather than later.
If you have uninsured motorists or personal injury protection insurance coverage then you should definitely call your insurance agent. You might also consider calling a products liability attorney to take a look at the vehicle, if the vehicle is still available. Other than that you should call an attorney to at the minimum and get some advice on what other options are available to you.
If this case happened in Texas then the statute of limitations is two years from the date of occurrence. You should determine the exact date of injury and contact a personal injury attorney as soon as possible. If it is not too late you have then have them file a lawsuit to preserve your claim.
As usual your child's health should be of first priority. The owner of the dog or even the store can have some negligent exposure for the dog. Typically, they dogs have to have some sort of history of behavior problems but it isn't always necessary to prove up a case. My office has handled several of these type of cases, but you for sure should consult with an attorney before talking to the store or the owner of the dog.
Generally, the answer is yes as many have already suggested. But you should not wait to consult a qualified attorney in Texas who has experience handling trucking cases. As soon as you were involved in this collision the trucking company had their own investigators on the crash site and they began preparing to defend their case against you. You need to have an advocate protecting your rights immediately.
Its possible. There has been some litigation in this area in the last few years. But as usual each case is different and a lot would depend on your damages. I suggest you contact a personal injury attorney to discuss your options.