Every so often, my SMS messages are held up (showing "sending") for a considerable length of time. I searched around and saw a hint that indicated that it may be because I'm also connected to my home WiFi for data when I'm here. It suggested that one tries to turn off WiFi connection to "release" messages.
I tried that and the 3 messages that were hung up immediately were "sent"...
Phone LG K8 V - using verizon messenger - 2-3 bars on Verizon cell network...
Connected to Exede high speed satellite internet. Sitting next to WiFi router...