Fire mage is a little weird: It is both the weakest mage overall, but in many situations, by far the strongest. Burst of flame is just outright busted (Range so large it is limited by the screen size, AoE, huge damage) and flame portal has crazy mobility. Against fire-resistant enemies, however, you will need to find some other abilities or use different tactics/strategies.
There are two tactics you could have used here. One takes no resources, the other uses some javelins.
The free option is to run to the stairs and go down. There is no requirement to kill everything as soon as you see it, or even at all. Using the SP (Speed point) you have, you could get out of range without taking damage, and then simply walk to the stairs. After that, there are many options, like finding a non-fire dmg spell at the library, or simply don't come back up - as a fire mage, clearing the core might not be a good idea.
The tactic to kill them all would be to use your javelins (an item to cause ranged damage). Javelins outrange fire lizards. If you use your SP you can get out of range. When you are 6 tiles away, they will be completely helpless, unable to shoot their fire clouds. Run around all the terrain in a large circle to keep that distance. Throw a javelin, then use a speed point to regain the tile you lost. Like this, you can kill them all without taking any damage.
While I am a huge fanboi (no denying that), is there any reason these tactics would not work?