Ok then, lets see.
What you want sounds cool, and after only playing for a month it's good to see you so interested in making something with it's own particular flavour. So, I'm going to try and help you out.
First, we've got to work out what we want him to do. You would like to see an increase in strength, and some fire damage. Ok, we can do that.
Now, if I was to put it together, we would have the following...
Now, this is a Prestige Class. It's easier to make a Prestige class to go on top of an existing class than it is to make a new class, and your DM is more likely to accept it as well. So we'll try this for a start.
Base Attack Bonus +5
Dodge, Improved Initiative
Rage Class Ability
Many barbarians are said to be in touch with their natural fury, yet few have wondered where that fury comes from. For a rare few individuals, they realise it's origin. The fury of a barbarian can be seen in the pure destructive power of a Fire Elemental. Having realised this, some try and focus on that inner strength, to bring it to the surface.
An Elemental Fury is not someone to be taken lightly. As they start in this class, they start to unlock wellsprings of strength, and small abilities with fire. Over time, these powers increase until he is the epitomy of a burning inferno. Overpowering to watch, and unstoppable up close.
2+int mod, taken from the barbarian list.
Base Attack Bonus:
Strong fort, refl. Weak will.
At level 1 an Elemental Fury gains the bonus feat, Improved Unarmed Strike. His class level counts towards his unarmed strike damage as if he were a monk of equivilant level. Thus, a medium Fury at level 1 deals 1d6 damage with his fist
At level 1 an Elemental Fury also gains the ability to go into an Elemental Rage 1/day. This ability can be used on top of his existing Rage ability, and the bonuses stack. He adds a bonus to his strength and gains the ability to do some fire damage. The number of uses per day, strength bonus, and fire damage go up over time.
At level 1 and at every 3 levels thereafter he gains another use of Elemental Fury
At level 1 the strength bonus is +2. This increases at 5th levl to +4, and at level 10 to +6
At level 1 the fire damage dealt by his Elemental Fury is only 1 point. This increases to 1d3 at level 3, 1d6 at level 6, and 1d10 at level 9
Note however that these bonuses only work for unarmed damage. His extra strength is only able to be channelled through his unarmed strikes, and his fire damage does not transfer to any weapon beyond his fists.
At level 8 an Elemental Fury gains the bonus feat Destructive Rage.
Now, this class isn't perfect, but if I put it up here, people can throw ideas around about it, and we can refine it.
In fact, looking at it a little closer, it's a little underpowered. So, we give him Fire Resistance equal to his class level, and maybe the evasion ability.
But it's all about starting with a base, and reworking it until you are happy with it.
Hope this helps!