new to prot warrior

[jolly crane]

The single biggest thing as to why you're feeling weak and almost died at multiple points in this log is because you don't have shield block up, especially during things like massive pulls when tank damage is at its highest. On the first pull, you sent a shield block once everything was gathered, and then you just

didn't for like 16 and a half seconds. That's more than its base CD (the CD on SB is reduced via haste), so you sat on a charge, especially since you never used the second charge until the next time you sent it. I'd normally say that means you aren't aware the shield block stacks its duration, but the next time you sent it and at various other points, you sent two charges back to back and got the extra duration. On top of that, there's a non-zero amount of talents you're getting minimal value from; thunderlord doesn't get very much value for Colossus due to generally not sending as many thunderclaps as Thane, so it doesn't reduce Demo Shout's CD by that much, really, and it looks like you're sitting on shield charge sometimes, which means you're losing out on SB uptime there, as well.

Basically, when it comes to high stress situations, you start playing like a BDK who hates pressing Death Strike

which is a pretty quick way to die

It's very notable when you contrast your hits block and taken with SB up:

Versus with it down:

You're taking roughly 25% of all hits coming at you without shield block up

Once we get past that, you're criminally underutilizing some of your stronger defensive CDs; Shield Wall is fine enough, it could manage to be used more (I haven't checked its actual usage, at least, just number of casts as fair warning), but things like Spell Reflection were used literally 4 times throughout the entire dungeon

That has a 20% magic damage reduction component which is often more valuable than the reflect component. On top of that, it's only on a 20s CD.

You would see a notable increase to your survival if you just started sending it on CD without even thinking about anything else due to how low its current use rate on your end is.

You're also sending spell block at very weird times; you could have had spell block for the first lieutenant in the dungeon, the one that thunderclaps, to at least help with DR on that any amount, but instead you sent it on the mob packs that literally only deal physical damage and cast no spells

I'd recommend peeking through Sense's document on Reflects/Blockable spells to get an idea where you can leverage spell block, since there's actually a good amount of spots where you can get value out of it in Priory. It's not as impactful as some other dungeons, but it does have value. You can find that doc here:
https://docs.google.com/spreadsheets/d/e/2PACX-1vQQCkBEkOadsvO4sTphB1RwzC6Z_3kq00IFaBrCk5Eagz2Jeoox7D7Rk3XwXMINbh4lUg9Vr-3RgoB2/pubhtml#

And it also looks like you're sitting on a lot of Shield Slam resets, since your casts feel decently low, which will cost you rage gen and, therefore, IP and CDR over time.

For a quick and easy feel-good fix, I'd recommend swapping Into the Fray for the other node on that choice node, Heavy Repercussions; your haste is a little low to be running ITF and be able to comfortably keep shield block up with fully proper play, so HR will make everything feel a lot more comfy. I'd also swap Thunderlord off into either Ravager or, if you really want to keep a focus on defensive power, Battle-Scarred Veteran

It should also be noted that Indom's healing has been hit a lot and is very impactful anymore, so you can also opt to drop that point in order to get the other you didn't pick up from above, so getting both Ravager and BSV at the cost of Thunderlord