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There are limited options to be able to get an immunization without a doctor visit. I assume that the location where you received the first injection is no longer an option.
The usual best option would be the local Health Department, but you have already tried this. I also assume that you told them that you had lab work elsewhere and they were not willing to accept it as justification for the injection. The next option for getting this at a reasonable price would be via your employer. Any employer in the health care field needs to have a mechanism for providing vaccines, as some are required by law to be provided by the employer. The employer may delegate this responsibility to a doctor or clinic, but there must be some mechanism. You can ask them whether this mechanism can be used for you to get the second immunization.
Otherwise, the only options are going to involve seeing a doctor. If you bring in a copy of the previous lab work you may be able to avoid further lab work, but it would still involve a doctor visit.