You have not disclosed the health reason why you need water, if it is diabetes which I would suspect, then you are protected by the ADAA and you are being denied a reasonable accommodation. You should document this issue completely and go to HR --everything must be in writing (email is ok) in order to protect yourself.
If you have a medical reason, and allowing you this is a reasonable accommodation, I agree that this denial is a possible violation of the ADA. Your needs, and the medical reasons for them, should be brought to the attention of the manager, and the Human Resources department, in writing. If the accomidation is denied, you should see an attorney.
Generally however, employers have a right to control the employee's food and drink which they are on duty, as well as control where they might partake in those things when they are on break.
To the PROSPECTIVE client, please call myself or another attorney for you choice with more detaiils and an appointment. My PRELIMINARY answer to your question(s) is for general purposes and based upon what little information you have conveyed. It is based on such limited information that the general answer should never be relied as a reason for your action or inaction. My response does NOT establish an attorney-client relationship and such may only be established by mutual agreement, and the signing of a written retainer agreement, which will generally require payment for our services, as this is what we do for a living and, just like you, we must get paid for our work.. .
If the employer's rationale for the rule is related to the business, and there are other methods of effectively accommodating your health-related need to have the ability to drink water during the work day (such as giving you periodic breaks, as needed, or during down times, to go to the break room), then the rule will prevail. One of the key provisions of the ADA and the regulations that implement the law, is that employees are not necessarily entitled to the specific accommodation that they want, if there is an alternative that is just as effective.
You should beware that just having "a doctor's note" does not necessarily always get you what you want. The doctor's note is subject to scrutiny by the employer, and the employer is allowed to get clarification from your doctor about the necessity for you to have a water bottle on your person at all times. In fact, the employer is also entitled to seek an independent medical opinion from another doctor to determine whether the "accommodation" of a water bottle on person at all times is really necessary.
You have not explained what problem, if any, there is with walking to the other side of the store to get a drink of water. That is an important issue, because if your doctor says that it is no problem, but it is a matter of what you want, and you don't want to have to walk to the other side of the store, then you are going to be out of luck when it comes to this issue.