Unfortunately, any two way comms requires both ends to be capable. You won't be able to make a phone call to someone without a phone and you won't be able to make a radio contact to someone without a radio. Simple. If you have a contact person who also has a 2 meter ham radio you will be able to find plenty of empty bandwidth outside the ARES dominated Em-Comms frequencies to make your contacts. The ARES net will be predominated by emergency comms at first but after the first 24 hours you shouuld be able to get Health and Welfare comms through them as the urgent comms become less overwhelming. Best bet is to make friends through the Ham community with some hams outside your area. That way you will be able to establish secondary communications directly. Of course it would be better if someone in your family / circle of concern were to get lisenced and equipped to the level you are.

Also, Join ARES. As a member of the net you will know when it is quiet enough for a moment to drop in some personal comms without over burdening the net and you will be part of those solving the problems rather than a victim representing a problem to be solved.

During the first hours of the ARES activation, net operators may reasonably not be willing to take Health and welfare messages for transmit since they will want to reserve the bandwidth for tactical Emergency comms. OTOH, if you are a net operator or even a station operator you will find moments of relative quiet on the net that will allow you to drop in some informal Health and welfare of your own without anyone thinking poorly of it. By net I mean the radio net not the internet.