Generally speaking in minor accidents you typically can. However, you do want to make sure if you are using health insurance you know what they have paid out in medical care otherwise you may be surprised if you settle a claim and they come knocking on the door asking for all of your settlement money.
Most sane people do not attempt to take on Fortune 500 companies part time while they treat and go back to work because they think they are going to save money.
The fact is research shows attorneys more than substantiate their value in personal injury claims. The time, effort, and hassle will be not be worth fighting a company that has you out manned, greater experience and training and focuses all of their time, energy and effort in saving money for the stockholders of the insurance company, which happens to be in direct opposition of what you are trying to do.