The rotation for a BLM differs a lot by level. When you read complaints of ice mages, they are referring to high level BLMs that only use ice spells, not low level BLMs. Everything changes when you learn fire 3 and blizzard 3. And your rotation will keep changing as you learn newer spells and traits.
Now, at your level, I would recommend you to use fire till you are out of mana. Then, when you are out of mana, transpose to go into umbral ice and regen mana. Use thunder once while under umbral ice and use blizzard till you have gained back all your mp
Now, transpose will still be on cd after you gain your mp back. I recommend you to just use fire right away and not transpose to astral fire.
Just fire all the way till you have no mp and then transpose. Use thunder and ice till full mp. Use fire till no mp. Rinse and repeat.
I won't explain about the newer rotations until you get the newer spells and traits (starting with Fire 3), since you probably wouldn't understand. However, once you learn Fire 3, just ask again and I won't mind explaining the newer rotations. Take note though that it changes very often from then on and you might be finding yourself changing rotation every few levels after that. It is quite easy to understand though. And definitely a lot more fun to play than low level THM.
Note: Of course, for all classes, getting newer spells means changing rotations. However, for all other classes, the basic rotation still remains somewhat similar. For BLMs, the rotation drastically changes, although the concept of using fire spells under astral fire for damage and switching to umbral ice for mp regen still remains.