Rats take a lot of time and responsibility to take care of. I have raised several and just adopted a couple baby girl rats this week. For one thing, you cannot only get one rat. A pet store will let you take only one home, but they get VERY lonely and will want to spend every moment with you, which they just cant. This will cause the single rat to become neurotic, and possibly angry. They will also become depressed because of this and they will not live as long.
Secondly, DON'T get your pet from a pet store! Find a breeder in your area who has recently had a litter that has two rats (of the same sex so you don't end up with unexpected baby rats!)available for adoption. They will live longer and healthier, and they are bred for temperament so they will be much friendlier. Pet store rats are almost always already sick, and are more likely to get tumors and die at a younger age. They have a proven shorter life span.
Next you need to make sure you can afford them, space, food, and time wise. Rats need to play outside of their cage multiple times a day for at the very least an hour at a time, and you need to play with them. This stimulates their mind and body and gives them extra exercise. This will keep them happier and healthier and they become more intelligent. Rats are very smart and need this stimulation. They also need a good, sturdy and large cage to live in, with proper hiding places, lots of toys, safe bedding, food and water. A pet store will likely sell you a hamster sized cage for a rat and sometimes even encourage you to use newspaper as bedding! Anything treated or with ink on it can be poisonous to them, and small living spaces make them depressed. The cage is supposed to be their home.
They also have a specific diet, including different types of grains, seeds, vegetables, fruits, and other dietary supplements. You cannot just but a rat or small mammal mix and feed them just that. Those do not contain half of the required nutrients for good health.
It is also important to get a few books on training and on first aid and other rat basics. If your rats get injured, it is up to you to take care of it so that they do not get infections or live in pain or discomfort. The training books are to teach them to come when you call their names, and a lot of other games to keep them happy and expand their minds.
There is much more also but I'm sure I am boring you and these are things that you should be able to research if you are truely interested in raising rats.
Once you have done the research (and feel free to email me if you have questions, I love rats!)you should have a better idea as to whether you are ready to take on the responsibility or not. Rats take a lot of time, love, and responsibility. For the record, I have also raised stick bugs, and this is a completely different type of thing. They cannot even be compared. If you really think you can do this, these are the types of things that you need to talk to your mom about. Tell her what it takes to take care of them (to the last detail!) how you would and could go about doing it, and make sure you actually can! If you don't have the time or interest to put in the time it takes to raise two rats, don't do it.
Also, if your mom says no maybe its just not the time. I waited until a couple years after I went to college to get my first rat. My mom also said no when I lived at home so I respected that and waited until I had the time and financial ability to raise and care for two rats on my own before taking on the responsibility of other lives.
I hope this helped!