It is normal for a three month old kitten to sleep most of the time. She probably slept less in the first day because she was uneasy of a new environment.
As given in the site - How Much Sleep Is Normal For Kittens?
A newborn kitten’s daily routine is made up of sleeping 90 percent of the time — that is almost 22 hours of shuteye!
Though it may not appear so, while your new kitten has peacefully nodded off, his body is hard at work. Development of his brain and central nervous system is dependent upon these frequent catnaps. Time spent snoozing in young kittens tones and strengthens the muscles and bones that give this species its athleticism and grace. Sleep even keeps your kitten’s immune system in tip-top shape. Without enough sleep, your kitten will become irritable and even at risk for infections and illness.
So, according to this article you should let your kitten sleep peacefully and not always try to wake her up and try to play. She is running away probably because she is extremely sleepy and you are forcing her to keep awake and play.
While the number of hours kittens sleep may seem excessive to new kitten owners, oversleeping in kittens is usually not cause to worry.
The only cause of worry is probably Fading Kitten Syndrome where among various symptoms gradual increase in sleep is one. But as mentioned here it is mostly common among neonatal kittens and possibly not possible to happen in a three month old kitten.
As given in the site - What Is Fading Kitten Syndrome and Why Do So Many Foster Kittens Die From It?
Profound lethargy, low body temperature, pale gums, low respiratory rate, and failure to root and nurse or eat are nearly universal signs of the syndrome.
But as I mentioned, it is probably not possible for a three month old kitten to have Fading Kitten Syndrome
Still it is always a good practice to have your pet fully checked up by a vet after you get a new pet. So if you are worried get the kitten checked up by a vet.