At level 11 probably don't have elven smithing.
So a leather shield a little more armor than hide but a little heavier. You can 'temper' the shield even if you do not have any smithing perks. Just buy or find a piece of leather and go to a blacksmiths table. Table tempers armor and shield. Grindstone tempers weapons.
Then click on the table and if you have a piece of leather and a leather shield you should be able to temper the shield. At level 1 that will probably only boost the armor by 1 or 2.
That would be the Flesh Shield, which you′ll find more easily in the game under the name of Lydia.
Give her loads of potions the next time (: You won′t find another shield with those lips
Go to any shop that sells shields.
If you see one better than your Hide shield, and you can afford it, buy it.