So, Shield Master doesn't, and shouldn't ever change your AC. If your AC was 19 with your shield before taking the feat, then it will be 19 after taking it, and it will not change.
A dexterity saving throw is not an attack against your AC, and has nothing to do with it; they are two different things. Your dexterity saving throw bonus is equal to your Dexterity modifier plus your proficiency bonus if you are proficient in the save; it will generally be a number somewhere between 1 and 6 for low level characters. You add that number to the d20 you roll when forced to make a dex save; the shield master feat lets you add an additional bonus as well - a value equal to the amount of Ac your shield provides, but it doesn't change your actual AC or do anything to it.
Firebolt is an
attack roll spell - the caster makes an attack roll (rolling a d20 adding their attack bonus), and tries to hit your AC. There is no
saving throw involved in this, so the shield master feat does not apply.
A spell like Burning Hands, on the other hand, does not make an attack roll. Instead, the caster simply casts the spell, and this compels those that are targeted by it to make saving throws instead; Burning Hands is a Dexterity saving throw, so this is where Shield Master would apply and allow you to avoid the damage if you succeed.
So, for example: Let us imagine that your character has 14 dexterity (a +2 modifier), is not proficient in dexterity saving throws, and has the shield master feat, and a shield.
If a caster casts a spell (that targets only them, in this case, let's say) that makes them have to roll a dexterity saving throw, they would normally roll a d20, and add 2 to this. With the shield master feat, they roll a d20, add +2, and then add +2 for their shield as well, which gives them a better chance of succeeding. If the spell was one that would normally let them take half damage on a success, they get to take no damage at all if they succeed. It's important to note that the shield does NOT help them if they fail anyway - they suffer the spell's full effects on a failure, as normal.
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That said, BG3's implementation of the feat leaves a lot to be desired.
"Gain a +2 bonus to Dexterity saving throws when wielding a Shield. If a spell forces you to make a Dexterity saving throw, you can use your reaction to shield yourself. On a successful save, you take no damage."
"Gain a +2 bonus to Dexterity saving throws when wielding a Shield." - This is a large nerf on the feat from 5e rules, since the original feat lets you add the AC bonus of your shield, not a flat number. Thus, if you have a +2 shield (adding 4 to your Ac), you would be adding +4 to your dex saves. This is a problem of Larian trying to cut down and simply wording without realising that it was worded a specific way for a reason, and weakening the feat in the process.
"If a spell forces you to make a Dexterity saving throw,"
The original feat applies to ANY harmful effect, spell or otherwise, that would have you make a Dexterity saving throw; if it targets only you, you can add your shield bonus to your save, but regardless you can still negate the damage if you succeed, even if the effect targets many creatures. So, for example... the original 5e wording lets you Shield Master a red dragon's breath weapon... BG3's rendition of it does not.
"On a successful save, you take no damage."
The original wording is specific for a reason: It applies to effects that let you save for half damage. If you are subjected to an effect that deals damage and has a negative effect, and it lets you make a dex save to avoid the negative effect, but you still take the damage regardless, Shield Master does not apply to it. BG3's rendition has lost this nuance.
