How do you measure whether an SMS campaign worked?

The delivery rate tells you whether your message arrived. It says nothing about whether it produced anything.

What you have anyway

Delivered, failed and opted out per campaign. Those three figures say something about the quality of your list and your timing, not about your offer.

The click

Put a shortened link in the message and you know who clicked. That is the first real indicator of interest. Use one link per campaign, otherwise you will not know which message worked.

What happened after the click

This is the figure that counts. Add a recognisable parameter to your link so you can see in your own statistics how many visitors came from that campaign and what they did. Without that connection you are measuring attention instead of results.

The figure people forget

Opt-outs. A campaign with a good click rate but a spike in opt-outs worked in the short term and hollowed out your list in the long term. Track that figure across several campaigns.