Unable to play all the Apple Music songs on my iPhone

I have Apple Music on my computer and phone. I pay a monthly fee for the service. I can play all of the songs on my computer. The same songs will not play on my phone. It says it cannot connect to server, or it just skips over them. I've tried all the suggestions I could understand. I'm frustrated and thinking of dropping Apple and going in another direction if I can't figure something out. Please tell me what I am missing.

[Re-Titled by Moderator]