I think that should give you some perspective on how your mother values and respects other living things. If you are a minor it is her responsibility to ensure any pet you get is cared for or she should not have allowed you to get it.
It does not sound like your gecko needs to go to the vet for illness, but in general one should never get a pet they can’t afford to provide standard veterinary care to. I suggest you try and do chores for your parents, relatives, or trustworthy friends of your family in exchange for a bit of money, so you will be prepared if your gecko does get an illness. Inexperienced keepers especially benefit from doing yearly wellness visits, just as you should do for a cat or dog. That way your reptile vet can guide you and spot any developing issues as early as possible.
It also sounds like someone misguided you in the extreme with regards to proper husbandry for leos. You definitely need to do your own research immediately to educate yourself regarding the bare minimum for leo care. At the least you should google ‘leopard gecko care sheet’ and read 4-5 of the ones that come up from reputable sources.
I have not finished my care sheet yet, but I will get you started: