Yes, agave. The itchy component is oxalate crystals, if I remember right. The itch will be unpleasant but then it will pass. If you can find some true Aloe vera, that should help. Images to steer you in the right direction:
Aloe Vera (Aloe vera)
There are maybe 500 different aloe species and not all are medicinal, so choose wisely.
If you want to tell the difference between aloe and agave, look for these signs:
* agave is generally more fibrous than aloe (usually you have to cut a leaf rather than simply breaking it off)
* agave generally has more serious spines (esp. the terminal one) compared to aloes
* aloes will flower every year; agaves do so once at the end of their life
* agave leaves start out longer and emerge from a sort of group hug at the center of the rosette, while aloe leaves emerge short and elongate later
* agave leaves have spines along the margins and at the end of the leaves (only), while aloes may have spines or bumps on the upper or lower surfaces of the leaf as well