You need to see an experienced elder law attorney. The information you received was both right and wrong. In addition to what the national and state law says on the subject, Medicaid practice can vary from county to county in one state.
What do you mean that you share an account with your mother? Does this mean that all of the money in the account is hers, and you are just a signer on the account for convenience? Does it mean that both you and your mother put money into the account, so some of the money "belongs" to you, and some "belongs to your mother? Who told you that her money can't be given to anyone? Was it some friend? Was it an attorney? Was it someone from the government who is responsible for determining Medicaid eligibility? When this person gave you this advice, how detailed were you giving this person information about the actual situation? All of these question, and more, are important in answering your question, but none of this information is provided. You can go to the National Academy of Elder Law Attorneys' web site to find an Eler Law attorney in your community. I suggest you do this.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship. Do NOT rely on anything I have written here -- You should contact a lawyer in your area immediately after reading my posting.
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I agree with all of the other attorney responses that there are definite planning options for your mother, but you need to sit down with an experienced elder law attorney to make sure that all of the facts are laid out and the best possible plan is devised for your mother's situation. The money saved will be far more than the attorneys fees that you spend, and literally one misstep in this area can cost your family thousands of dollars. This is not a DIY area!