New to Black blue mill decksthis is my idea for a deck

any tips are welcome

Psychic Strike is, a surprisingly good counterspell. Not only does it counter, but it also mills. Szadek, Lord of Secrets may seem good, but it comes out turn 7 and even then only mills for 5, (Tome Scour does this for 1). Duskmantle Guildmage is another one of those mana intensive cards where casting spell instead of activating an ability might have been a better idea.

I love when people put their own spin on a strategy. Good job so far.

One last thing: I realize that you wish to keep it budget, but Glimpse the Unthinkable is an amazing card (which is why is costs so much).

Jushi Apprentice if you can get to 9 cards for a second.

Glimpse the Unthinkable if its in your budget Breaking / Entering if its not I'm also a huge fan of Sphinx's Tutelage with card draw spells like Visions of Beyond. Hedron Crab is a solid one drop especially if you are running fetch lands. I personally run Keening Stone as a finisher

I like Dimir Infiltrator, also since you have Duskmantle Guildmage I would include Mindcrank for the infinite combo.

Hedron Crab and Jace's Phantasm should be your only creatures in mill decks... If you don't have enough mill cards then you wont win, if you want to win off of forcing your opponent to deck themselves. I have also seen Startled Awake  ^Flip in a friends mill deck, and it is a fun card. Archive Trap is also a ton of fun and can result in a turn two or three win if you have all 4 in hand and chain them together. It can get crazy.

If you want to win on damage more than mill, then Nightveil Specter is also a fun card that supports both strategies. Also, Tasigur, the Golden Fang would also work seeing how many spells you want to cast.

Tome Scour and Thought Scour are also musts in budget mill decks... Traumatize is also a cheap card in dollars, but not so much in mana.

To bring him up again, Hedron Crab plus any fetchland is super cool. This can be the expensive fetches (i.e. Polluted Delta) or just Evolving Wilds. Fun interaction, turn 1 crab, turn 2 mill for 6 plus a 1 cmc blue mill(Tome Scour)... in short, turn 2 mill 11, plus their original 7 and draw, so on turn 2 they're missing 20 ish cards.

Extra removal could be Murderous Cut.

All of these are just suggestions though, but I think they are definitely worth looking into!

I agree with BlackCoffeeMagician on the Sphinx's Tutelage. It's a great card that works well in most mill decks.