No. Once you settle a personal injury case, whether it’s on your own with the insurance company, or if you have a lawyer, you cannot ask for more money. During the settlement process, you will have signed a document, generally called a “release” (or “release of all claims,” “settlement agreement and release”).
There are variations on what it’s called. What that document says is that the insurance company for the at‑fault party, if they’re self‑insured, has paid you this money in exchange for this release, and that you’ve agreed to accept it by signing the release. You release the at fault party and their insurance company and waive all claims you have when you sign a release.
This is all you can ever get as a result of this particular accident and your injuries. You cannot get more money later. You should only settle once you have finished your medical treatment and have a good handle on all your damages such as medical bills, lost wages, and loss of future wages.
After you settle and sign a release, you cannot go back and get any more money.