I am a 21 year old student, dark inner thighs is my problem. My thighs are big. There is no gap between my thighs

Without seeing a picture I am going to make a guess that you are darker skin complexion, as patients with darker skin tend to have more melonocytes and produce more melanin to cause the hyperpigmentation between the thighs.   First thing we have to do is reduce the friction between your thighs.   There is a reason why our knees and elbows are slightly darker then the rest of our body, and it is due to friction and pressure which will increase inflammation which stimulates your melanocytes to produce darker pigment for your skin.    You can treat the pigmented area with laser but it will return very quickly unless you remove the cause. 
Then you can choose many lasers out there to remove pigment, usually Q-switch laser is best for darker skin complexion.   We have the Lutronic Spectra laser and we charge $300 per treatment.