Exception Magic Item Creation Help.. Suspense 24hours

Well my DM said I can make one exceptional magic item for my character and I wanted to know if anyone has some ideas that will assist me.  I can do it, but what if someone else throws out an amazing idea.  The other party members, (2 fighters/2 clerics/1 rogue) have one exceptional item each and I’m just now bringing my character back to the party as she has been away so they know she is… the weird one.  My character is a Human Wild Magic Sorcerer, with a focus on ice magic.  The aesthetic of the character is that she cuts herself and uses her blood for casting, so her spells are frozen blood.. red ice essentially.  It is purely cosmetic, but it creeps the party out.  She always wears a mask.  Lastly we are going into the underdark, where undead and Drow are, so to say fights are very hard is not an understatement.  My character is the squishiest, lowest AC and HP.  Any help on an item would be great, or just a cool concept of an item.  I currently have no magic items.  Below is other exceptional items that the party has as a reference as to what others have or had options.  I just got told today, and have till Monday when game starts, apologies for the time crunch.  Again thank you to anyone who posts ideas!!!!

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Klavek Moonblade

Light. If the sword is on your person,
you can use to it cast light at will.

Moonbeam. Once each day, if the
sword is on your person, you can use
it to cast moonbeam (DC 15 or your
spell save DC, whichever is higher.
.......
Eagle Eye Bow

+1 to attack and damage

Eagle Eye (2/day). If your attack
roll hits, but you did not roll a 20,
you may roll the attack again. If
the second roll also hits, you may
treat the attack as a critical hit.

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Healer’s Mace

Mace, uncommon (requires attunement)

This mace functions as a holy
symbol for a servant of a deity
associated with life or healing.

You gain +1 to attack and damage
rolls made with this weapon.

Font of Life. If the mace is on your
person, when you cast a leveled healing
spell (such as cure wounds), the mace
gains a charge. The mace holds
up to 3 charges. While holding the
mace you can expend 3 charges to
cast mass healing word, 2 charges to
cast prayer of healing, or 1 charge
to cast cure wounds. Expending
a charge to cast a curative spell
does not charge the mace.

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Wightstaff

Quarterstaff, rare (requires attunement)

This staff is carved in the Vikmordere
style, eliciting spirits from the
wood’s natural patterns. Images of
death—skulls, bones, and ravens—
adorn the length of a wightstaff. The
staff functions as a holy symbol for
a servant of a deity associated
with death or necromancy.

You gain a +1 to attack and damage
rolls made with this weapon.

Death Spirit. If the staff is on your
person, when you cast a leveled spell that
deals necrotic damage (such as toll the dead or inflict
wounds), the staff gains a charge. The
staff holds up to 3 charges. While
holding the staff, you can expend
3 charges to cast animate dead, 2
charges to cast blindness/deafness,
and 1 charge to cast false life.
.......
Imperial Chainmail

Armor (chainmail), uncommon

This suit of Klavek chainmail is
flawless. At dusk each day, the armor
casts mending on itself.

You gain a +1
to AC while you wear this armor.

.......
Stormshield

Armor (shield), rare
(requires attunement)

This large iron-banded wooden
shield is etched with runes. The
shield functions as a holy symbol
for a servant of a deity associated
with storms, lightning, or thunder.

While you wear this shield you
gain a +1 to AC and resistance to
lightning and thunder damage.

I have a couple questions to clarify first if you don't mind. First, were you given a specific rarity or max rarity you could make the item? Second does your group tend to go lighter on homebrew, or heavier on homebrew? Third, was there any specific areas you think your character could use some assistance?

Some vague ideas before you answer my question: a better spell modifier bonus/save, access to a spell you don't normally have, unique mechanics that lend to your character's blood ice flavor, maybe adding an opposing duality to the blood ice

Edit to add: A more interesting idea I had is perhaps there could be some sort of mechanic where as an action you can choose to sacrifice as many hit dice as you want, essentially badly bleeding yourself. You then roll the number of hit dice being sacrificed and either do a singular powerful attack, or maybe a 15ft cone attack with the copious amount of blood ice you'd then have.

Idea 2: Or perhaps instead an item that the lower your health gets percentage wise out of your max, the more damage your spells do. Empowering your ice spells (and other spells) in a similar way to my other idea.

On top of what ColesCoal said, sorcerers don't have proficiencies to martial weapons or any armor or shields. I would not try to think of concepts for magic items that your character doesn't have proficiency with unless you're designing the item to someone else. That still leaves simple weapons, rings, scarfs, boots, clothes, etc. available, so there's plenty of options.

Those are some great ideas!  I also was thinking of an item that I take damage, representing loss of blood, and it would empower my spells (and potentially begin to replace my blood with something else).  

as for your questions.  

I do not think there is a max rarity, however we are level five and all the items were limited to +1 items.  So my guess is that is the area/limit to it’s ability is that level range.

So far this is the only homebrew is the items.  Everything is by the book.  We were restricted to 5.5e subclasses.

Where my character would need assistance is, avoiding getting hit.  Fights are tough, previous low ac cleric was like a pin cushion.  If your doing damage or healing your a high priority target, and every drow got a bow or ranged spells.

Thanks for responding 

That is true.  I was looking at a ring or some other item.  I had an idea thst it would be a ring and would do a charge system, but with cold much like the above items.  Then the charged spells would give me access to spells I don’t have like armor of Agathys.  However taking damage to do additional damage that was mentioned by ColesCoal gives me some thoughts