I don't think there is any fundamental right to sue private parties in the US. If you find it, please post about it.
That being said, the constitution has established an independent judiciary which has little limit to what matters it can opine. You have a right to petition that judiciary. You're somewhat correct in that you don't have a right for them to listen.
I don't think that's actually true. IANAL, but IIRC the jurisdiction of the federal judiciary is quite limited compared to that of the states.