Some days you just can't shut out the distractions or resist the temptation to go to the latest message that just came in.
iPhone with fewer distractions:
There are a lot of options that might apply to different situations.
Face down
The simple one (if you don't wear an Apple Watch) is to just lock your phone and place it face down on a table. This won't prevent all notifications, but it does reduce how many will make a noise and interrupt you.
Mute group chats
In case you didn't know, you can mute a group texting chat. You won't be able to see the messages until you open the Messages app. But a group can go down a terrible rabbit hole and suck you in with it.
Turn on Do Not Disturb
There are a few options if you want to have your alerts come back on automatically. You don't have to risk forgetting to turn it back off. And having an appointment gives it even more options.
DND Settings
You can still allow calls from favorites. And there's an option for the second successive call from the same caller to breakthrough Do Not Disturb.
Automate DND
You can use the Shortcuts app to automate when Do Not Disturb comes on, say, when you open the Books app to sit down and read.
Android Do Not Disturb
Android isn't my specialty, but I did find a nice guide to customizing Do Not Disturb on Android. I use their sister site all the time and respect a lot of folks over there.
Hopefully this has given you some ideas to get you going. Work Well!