A few options to consider:

(1) move the app to show at the bottom for mobile.

(2) use custom padding inside the app to move it downwards.

(3) try using "fixed" placement instead of "sticky".

Didn't work?

Try these alternative apps:

https://apps.shopify.com/quick-announcement-bar-always-keep-your-customers-informed

https://apps.shopify.com/yeps-io