I'm building a barb monk and the char sheet doesn't seem quite right. My AC says 14 which means it took my monk unarmored feat into place when I want it to use my barb's unarmored feat. 

I think the char sheet on dndb assumes that the player will choose the monk unarmored defense over the barb's but what if I wanted to use a shield with the intent of  getting the feat that allows me to shove with it?

https://www.dndbeyond.com/profile/Pochusaurus/characters/21744010

So two things. 1. with how your character's stats are, the monk AC and barb AC+shield are actually the same(2+2 vs 1+1+2). 2. The monk AC cannot be used here anyway since that strictly forbids a shield, while barb does not. One other thing, when a character has 2 or more usable options for how their AC is calculated, dndb will always default to the one that results in the higher number.

Quote from DootNoot1 >>

he monk AC cannot be used here anyway since that strictly forbids a shield, while barb does not.

To clarify, the Barb's unarmored AC is 10+Dex+Con. Your character has a +1 to con and +1 to Dex, making your Unarmored AC 12. A Monk's unarmored AC is 10+Dex(1)+Wisdom(3), making your Unarmored AC 14. With the shield, your Barb's defense would come into play and match the AC of 14.

However, the character you shared is a level 17 monk. in order to benefit from any of the Monk's Martial Arts ability, Unarmored movement ability, or Unarmored AC it specifically states you cannot be wearing armor or using a shield. By wanting to wield a shield and use the Shield Master feat, you'd be effectively crippling your character.

Unarmored Defense

Beginning at 1st level, while you are wearing no armor and not wielding a shield, your AC equals 10 + your Dexterity modifier + your Wisdom modifier.

Martial Arts

At 1st level, your practice of martial arts gives you mastery of combat styles that use unarmed strikes and monk weapons, which are shortswords and any simple melee weapons that don’t have the two-handed or heavy property.

You gain the following benefits while you are unarmed or wielding only monk weapons and you aren’t wearing armor or wielding a shield:

Unarmored Movement

Starting at 2nd level, your speed increases by 10 feet while you are not wearing armor or wielding a shield. 

Hey so just a tip if you want to go STR monk a cool race is Tortle as you get a natural AC of 17. You can put all your ASI's into STR and WIS. How did you do do stats?