In Wisconsin a client's file is simply that - the client's file. You can take the file and go to any law firm you'd like. Your previous attorney may have a lien for attorney's fees on the case. That's only fair because they did some work for you. If you hire a new attorney that new attorney would work with the previous attorney to apportion the attorneys' fees earned between the two firms. The total fee (usually 20% for Workers Comp) would not increase. Each firm would get a portion of that 20%.
First, I would recommend you call your attorney and sit down in her/his office to get fully informed about the strategy and the reason they recommend accepting the offer. Most cases have risk involved. You need to know the risk going forward. Maybe the risk is too great to not take the offer. But, in order to know the risk you need to sit down with the lawyer and get on the same page.
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You can switch attorneys, but as a practical mater it may be difficult to find another one to get involved since the attorneys will have to split any fee. You may have a claim that is worth more than the $20K setlement, but not knowing the facts of your case or the extent of your prior medical history, it's hard to say whether the offer is reasonable or not. There are always risks with trying the case. You could lose - no matter how strongly you feel about the legitimancy of your condition as being work related. I'd sit down again with your attorney and have him/her set forth a best/worst case scenario. It seems to me there are issues that are causing this neck claim to be valued at only $20K.
This advise is given in a general sense, since all relevant facts are are unknown. Contact an attorney so you can explore all concerns relating to your particular legal situation.
I agree with the other comments. Your current attorney knows you case the best and should be able to explain the risks /rewards of trial and the likelihood of winning. On the merits, however, keep in mind that cannot get your neck covered unless your doctor is willing to testify that your condition is related to your accident. In illinois, related means caused, aggravated or accelerated your condition. WC already has IME so you must have medical support to have any chance of success.
You are entitled to a clear and understandable explanation from your lawyer as to why he thinks that settlement offer is acceptable. This is what you have him for--to analyze your claim and give you advice. Make an appointment to go in and sit down with the lawyer and discuss this in detail with him.
This answer is intended as general information and not as specific legal advice. If you want to have a free consultation with me, please contact me through AVVO.