Nope. I beat the game the first time around doing more or less that. Of course, there are a few things to consider. First, you probably should invest in block or at least attempt to block from time to time. Hard hitting enemies do enough damage that a block can really help before your armor is at a useful level. If you need a free way to train it, grab a shield and make a few of those long term regen stamina meals and then track down a few foes. Dispatch all but one, eat whatever foodstuff you brought that has constant regen stamina and bash as quick as you like. It raises this skill incredibly quickly and for anything human (or about the same size) you can generally stun lock them until they die. Just don't invest in deadly bash before doing this or the enemy dies quickly.
Other things to consider: two handed weapons are staggeringly lethal. It is easily possible to deliver 900+ damage per normal swing if you play your cards right (and fiddle with enchanting, alchemy and smithing). Enchanting in particular is an excellent friend when it comes to damage as you'll want to get extra damage out of your giant killing device.
Finally, generally when you have a problem in Elder Scrolls, it is not the result of a bad idea on how you're going to approach the game but rather the result of gaining lots of secondary skills that force you to level beyond what you should. In the end, those support skills that are super easy to level up are a terrible burden if you aren't careful and enemies will quickly be able to overcome your armor and shrug off your hits. In the worst cases, one could end up with newbie combat skills yet be level 40 because they farmed sneak/pickpocket/speech.
All that said, I expect that given your level and the enemy in question that you've encountered problems on the road to High Hrothgar. Trolls are some of the most "difficult" enemies in the game - they're tough to stagger, they regenerate quickly, they soak up lots of damage and they attack with quick power attacks. Couple that with the fact that they can generally outrun you and you have a problem for a low level character. This makes the decision to have at least one Frost Troll on the road to High Hrothgar, the fourth quest in the game, really silly.
As such, I have a number of suggestions. First, join the companion's guild and complete the questline. In addition to getting some decent loot (including armor of similar stats to steel only lighter) you get free training in heavy armor, two handed, archery, one handed and block (you have to ask the trainer to follow you (which lets you access their inventory), then train, then retrieve your gold). A few levels of that can help bring up your skills to what they need to be. If you're having a problem with simply not being able to absorb damage, also consider finding the Lord Stone which grants a significant amount of protection to magic and physical damage. If magic is a problem, go to Riften's Temple of Mara and do the Book of Love quest - you'll get an always on +15% Resist Magika power.
also the shield deflects a lot of damage from their breath attacks
