am I right to be mad?

You have a right to feel like your needs are not being met... But if your mom is going to favor your sister over yourself, you need to come to terms with that NOW and not let it fester in you like it does in so many siblings.

You should make a vocal pronouncement that since your mom likes your sister more, you are going to save up for a desk yourself and ask for an increase in your allowance or ask to be allowed to get a job, something age appropriate.

Then, spend time looking online, preferably while your mom is watching, picking out a desk that you want so you will know how much to save up for.

Staples.com, Ikea.com, Walmart.com, Target.com, OfficeDepot.com etc. etc. etc. then print it out, tape it to the door of the fridge, then keep a running tally on how much you have saved up for it.

If your parents see how important this is to you, they might help out or at least stop playing favorites.

If I were you, I would be MAD. That isn't fair, and a desk is a useful thing, that you can use everyday, and lasts for a while. A little thing for lotions, and makeup is NOT a useful thing. It is, but she can live without it. The lotion and make up thing, shouldn't be bought for your sister. Your mom, should buy you a desk. You deserve it. Where else are you going to do work, and stuff? If I were you, I would talk to my mom, or write a note, email, text, or call on the phone. Good Luck :)

It's most likely a bag and that isn't quite as expensive as a desk would be. Of course you can be mad but you need to acknowledge that your mother isn't saying "you don't matter" for buying a bag (or a cheapo organizer) for your sister. Maybe the bedroom doesn't have enough room to have a desk to begin with or if you get one, sister has to get one as well so she doesn't use yours - etc. The best thing you can do is shop around to find cheap (but sturdy) desks that you can present to your mother.

I think there is not enough space to fit the desk...

Yes, cuss yo mama out