If you were on a healthcare plan through your spouse's work, you will typically need to find your own widowed healthcare plan immediately.
When a spouse dies, it is considered a qualifying event, and as a result, you can sign up for healthcare plans regardless of whether they are in open enrollment.
You may want to talk with your employer about getting a plan through your own job. If that's not an option, the healthcare exchanges may have a good plan for you. Widow(er)s with children may automatically qualify for low or no-cost health insurance through programs like TennCare.