Frost Titan (there is also Icefall Regent) should be your finisher of choice as it is much better than your current ones. Gideon Jura is another finisher you should have in your deck as it helps with removal and can soak up a big attack.
If you could add more a expensive card then Tamiyo, the Moon Sage would be a solid addition.
Seal Away is a good removal option, it is like Swift Reckoning with "spell mastery" which exiles (with the downside of being susceptible to enchantment removal).
For mass-removal Settle the Wreckage can be very good exiling a big alpha strike against you.
Gideon's Lawkeeper is better than Niblis as you don't need to attack with it to use the tap ability (meaning not being able to tap opposing attackers before the "declare attackers" step) and also costs only 1-mana to cast. Ojutai Exemplars can be pretty good as well as it has many useful abilities with tapping creatures among them when you cast non-creature spells. Niblis of Frost has a similar ability, it actually freezes after casting spells.
This deck isn't on par with what is played in Modern (unless it is super casual).
If you are looking for a budget Azorius Control deck you should check out the budget section and maybe open a thread there.
Gideon Jura is another finisher you should have in your deck as it helps with removal and can soak up a big attack.
If you could add more a expensive card then Tamiyo, the Moon Sage would be a solid addition.
Seal Away is a good removal option, it is like Swift Reckoning with "spell mastery" which exiles (with the downside of being susceptible to enchantment removal).
For mass-removal Settle the Wreckage can be very good exiling a big alpha strike against you.
Gideon's Lawkeeper is better than Niblis as you don't need to attack with it to use the tap ability (meaning not being able to tap opposing attackers before the "declare attackers" step) and also costs only 1-mana to cast.
Ojutai Exemplars can be pretty good as well as it has many useful abilities with tapping creatures among them when you cast non-creature spells.
Niblis of Frost has a similar ability, it actually freezes after casting spells.
Authority of the Consuls/Blind Obedience is a decent option to make opposing creatures enter tapped.
Send to Sleep can be a more efficient Frost Breath with "spell mastery" and Sleep (and Blustersquall as an instant) can be a decent mass-tap spell.
There is also Feeling of Dread which offers 2x tap spells in one card.
If you're looking for good card draw spells then you have:
Anticipate/Shimmer of Possibility as cheaper ones and Fact or Fiction (and Glimmer of Genius/Hieroglyphic Illumination/Chemister's Insight)
as a more expensive one.
The are also cantrips that tap creatures like: Niveous Wisps and Expose Evil/Repel the Darkness.
A straightforward and efficient approach is a combination of removal and countermagic and this is how conyrol decks in modern play.
Maybe something like Pauper is more suited to this type of deck though I doubt it.
If you are looking for a budget Azorius Control deck you should check out the budget section and maybe open a thread there.
I've recently build a 100$ UW Control deck myself.
Here it is - https://www.mtggoldfish.com/deck/2179446