I'm landing my e's on her, the problem lies in the fact I can't keep her slowed because of her shield so she ends up ranging me back to her turret, or she'll drop down her aoe on the creep wave and get a large chunk of her hp back with her passive. Even with hammer she never let me really get in range of being able to auto attack.

That said my normal build for Urgot is as follows.

Brut
Ionian
Hammer
Atmas

Thats my core and I build around whatever is needed. I can pick up the mr because I know she won't kill me outright because by mid game urgot gets pretty tanky with this build. The problem is I just can't do anything really to kill her it's like playing against a tanky soraka. Basically her shield blocks the slow mechanic when I land an E and then Q with my shield up.

So basically Morgana is one of Urgot's counters to bot and my best bet overall is to just switch to top. Sad face

Morgana's shield blocks the slow from Urgot's shield but doesn't stop the Noxian Charge from locking on or the damage from his Acid Hunters. So once you hit that Noxian Charge hit her with as many Acid Hunters as possible, and save your shield for when her's is on cooldown. Early game harrass her as much as possible while keeping that minion wave under control. Since she can destroy minions quickly it is easy for her to push. Urgot doesn't really get good pushing power till he gets some damage icons, but then a Noxian Charge and a couple of acid hunters will kill waves fast.
I usually stay near my minions so they block her trap, yes I know she can just throw down her pool, but that means she has to get in range of your Noxian Charge. Just zone her with that, if you land it chase a little and launch those Acid Hunters. Its hard to actually take her point unless you kill her, but unless are losing top or can kill her easily it is more important to protect your point then to risk pushing hard and getting ganked or killed.
I still don't understand why people say not to get TotG on Urgot, it's a great item giving you plenty of Mana, and once its upgraded to Manamune the Mana and Attack are great. I don't get Lifesteal much just cause you have to use his auto-attacks and his range is horrible. I would rather get something with Spellvamp since it works with his Q.
Try to play against her as much as possible to learn, I like to 1v1 friends to get good against champs I am not sure about.