Sorry for raining on your parade, but those "lucrative" nursing jobs
require significant levels of experience & expertise. There is a direct link between the eligibility requirements and level of pay - in any profession. With only 3 months of experience, you are still a new grad as far as acute care jobs are concerned. This may be different for LTC, but I don't know for sure.
Public health is essentially a tax-supported, governmental indstry so it is not an area of high salaries; these jobs may be subjected to long periods without any increase if there are more pressing budgetary needs. I recently heard that Louisiana was eliminating funding for childhood immunizations (!!!) due to budget shortages - nuff said.
If you are interested in climbing the career ladder to nursing administration, you will need an MSN, as well as well-established clinical competency & history of jobs with progressive increases in management accountability. Once you leave direct care, you will be salaried, with no opportunity for overtime or premium pay despite working >40 hours a week. It is not unusual for the lower levels of 'management' positions to pay less than staff nurse jobs. It can be a pretty hard slog.
It is not about "connections". Your network may help you become aware
of job openings, but hiring is based upon experience & demonstrated expertise.