Hey, it is very common to take SSRIs to treat anxiety.
If exactly Fluoxetine will help you, nobody can say. Drugs never work the same on different people, thats why there are so many antidepressants out there.
I dont want to scare you (your picture looks like youre scared btw

), there are threads in the recovery section where SSRIs made the cure possible. For me, it decreased the anxiety and the thoughts that made me more anxious where gone. For others it did nothing. I just want to be realistic
Your doctor told you SSRIs take time to have an good effect? Sadly some people first notice only the withdrawals, thats why some stop taking it before the good effect can start. Make your own experience and find out what is good four you!
Hope i could give you a good answer and some hope!