The (standard) fee for a contingency case is 33% or 1/3. Now (if) the case goes into a lawsuit, then the fee usually goes up to 40%.
And yes with any personal injury cases, most lawyers will tell you have a great case so that you will sign the contract agreeing to the fees. Let me guess that this lawyer you hired advertises on TV or on billboards? If so, they are called ambulance chasing lawyers, that charge more, (to pay) for their advertising that costs too much from the clients.
And yes, not surprised that this was settled between lawyers in 3 months, since guessing you had an easy case, like a rear end, or hit by a drunk driver, so they paid quickly.
What most people don’t know that when a lawyer handles your case, they send a letter to the insurance company or the lawyer on the other side. All settlements are usually done by telephone or by mail/e-mail. They (rarely) go to court and they get all your medical bills, medical reports from the doctors that treated you and then submit the demand to the insurance company or to the other lawyer to settle.
As for him stating not a good case later, most likely meant he knew he could not get any more money, so suggested you settle, (otherwise) if not, then he (might) have to file a lawsuit and wait a year or more to settle.
A personal injury case is (reimbursement) of the medical bills, “any” lost wages then (adds) pain and suffering. So if, after the medical bills are paid and the (pain/suffering) is less to you vs the lawyer means that the lawyer took the (gross) meaning the total amount of the medical bills and divided by ½ (50%) then odds are that the lawyer was paid much more than you.
retired auto adjuster that was married to a lawyer (deceased)