So, I wanted to build a character who is based off the idea of a Paladin: heavy armor, melee combat, also a powerful healer. Only level 4 so far, but from what I can tell it seems like my healing aspect is doomed to be really weak.

I made a Redguard born under the Warrior sign. I have 63 Strength and 71 Endurance so far, but only 34 Willpower and 32 Intellect. My initial heal spell is already really weak, and it only gets weaker as my endurance goes up. But I don't have enough Magicka to use the next step up (which would need my entire magicka bar to cast anyway. I have about 60 right now, it costs 64).

Is it even possible for a Warrior playstyle/build to be proficient as a self healer? And yes, I did choose Restoration as a Major Skill, if you wonder.

What are your majors and minors? In order to increase your Magicka you need to increase your Intelligence. If Alchemy and Mysticism are Minors create lots of potions and pick up a Detect Life Spell and start casting it. Then use Intellegence as your 3rd choice on level ups.

When I think warrior build, I think alchemy for healing. Alchemy is much easier to max out than restoration, which takes a very long time. If you are a powergamer then you can max levels and attributes.That way, restoration is easier to use and you'll have 200 magicka. However, if you have chosen to underlevel, then you may not get the strong warrior you want and max intelligence.