Can you give us more information about this character? What's your armor rating? What's the damage output of your warhammer? Do you have potions that you can use in the middle of the battle? What's your Magicka:Health:Stamina like? Can you tell me the name of the location if you remember? I think you might have to put in under spoiler. What's your Heavy Armor skill level? Two-Handed skill level? How many perks do you have in those two trees?
I think using potions is very helpful for melee characters. It's like a free reset button without having to start over. You go from 30 health to 400 health instantly. I think good melee players are not afraid to use potions. Use them liberally. You can always buy more at potion shops. You don't have problems with money do you? At level 37, you probably have more money than you know what to do with. You probably should be able to buy everything at the potion shops in 5 cities without blinking. Do you have vegetable soup? All good melee characters carry vegetable soup, right? Also remember that you are a dragon born and you have shout capability. I think whirlwind shouts are very useful for closing distance quickly or running away. Very powerful for melee characters.
Here's everything you asked for:
Armor rating = 579 w/ shield - 499 w/o. Warhammer damage = 83 base + 15 extra fire damage. Yes, I routinely use potions or apply poisons to my weapons. Magicka = 100, Health = 343 (modified), Stamina = 246 (modified).
The location was
Spoiler Uttering Hills Camp for the miscellaneous sidequest "Explore Uttering Hills Camp and recover the Elven Mace of Despair."
Skills - Smithing = 85 (highest perk: Ebony smithing), Heavy Armor = 77 (Juggernaut 4/5, Well fitted, Tower of strength, Matching set), Block = 52 (highest perk: none), Two-handed = 82 (Barbarian 5/5, Champion's stance, Skullcrusher 2/3, Great critical charge, Devastating blow, Sweep), One-handed = 47 (highest perk: none), Archery = 60 (Overdraw 3/5, Critical shot 1/3), Sneak = 74 (Stealth 1/5, Muffled movement).
No, I don't have any problem with money since I loot everything I can (of substantial value) and then go back to towns to sell it all and/or improve weapons and armor. No, I don't have any vegetable soup, but I'll make some since I have enough food as well. And I use my shouts as much as I can. I have the amulet of Talos which helps reduce the time between shouts. I alternate between that and the Gaulder amulet which adds another 30 points to my magicka, health and stamina.
Have you tried a battlemage? They are not exactly a wuss at close up combat, but the idea is to keep the enemies at a distance.
My biggest tip is to lvl up as evenly possible with your skill's, IF something get's to outa wack, you end up with 1 shot dead. I noticed this with my battlemage took a look at his lvl's on everything and noticed how low his armor was compared to other thing's. so I went out and "picked" fight's with wolves and whatever crossed his path not using magic up close and personal til his armor rating started to go up.
I think I'm being consistent with balancing out everything. I'm definitely not over-powered in any one skill. I think I did make a battle-mage character before but never played him that much because I ended up making different characters.
I don't know where you are going, but I find some areas more difficult than others. Whiterun area is pretty easy, while heading north to Dawnstar can be a challenge depending on what level your character is.
Check the spoiler above for the exact location.