Iphone restore backup isnt working, says theres not enough space when there clearly is. Please help :(

So! Long story short, somehow alot of REALLY important text messages got deleted off of my phone recently, but thankfully I backed up my phone on itunes a week prior to that! I tried to "restore the backup" onto my phone but it says that theres not enough space. I have deleted so much stuff already so I KNOW it has alot of room on it. Can anyone help me out here? I really need those messages! plus, there are some really special ones from my mom on there as well and shes very ill and I would be so heartbroken if I lost those!😢