Is Urgot incredibly hard to kill or just a problem for me?

It's working as intended.

You basically can't burst him from melee. His kit heavily revolves around "you're in my reach, I'm going to kill you quickly" while being abnormally tanky. Your best bet is to poke up down with kills before trying to all in. High ap ratio burst mages like Lux or Syndra can lock him down and tear him apart, while dash in > kill champs like Diana struggle against him in a 100% hp 1v1.

You just have to learn his techniques and adapt to them, and above all, remember that he counters approx. 70% of the current top laners, maybe more. If the enemy top laner picks urgot, you want someone like Vayne, Darius, or Cho, who can shred his health. (Darius mostly because hemo 5 > ult is essentially a guaranteed kill except on hard tanks, plus the Q sustain and E lockdown)

A lot of it is the W shield, which is actually huge if he has any bonus HP

The W shield is a bit high for the cooldown

Tryndamere is always an option... the best way to deal with Urgot is to negate his poke with Tryndamere's innate sustain and farm until Urgot unintentionally pushes in too hard, before going in and wailing at him because he can't actually kill you. Urgot's kit makes it rather hard for him to freeze and Tryndamere can last hit really well under tower. Tryndamere's ult also flat out says no to Urgot's ult and therefore, Tryndamere can just win because the rest of Urgot's damage is a consistent drain of his opponent's HP. Also, Urgot is not as mobile as Tryndamere so it is easy for Tryndamere to get away if he takes more damage than he wanted to.