Should I give up on fluoxetine ?

Hi, krisia!
You say it doesn't seem to be working and I wonder if you've seen any improvement at all? More energy, better appetite, better sleep? If you have then a dosage increase is warranted.
The full benefits of the medication may not be felt for at least 6~8 weeks and for some people it may take a bit longer.
You must have told your doctor exactly how you're feeling and if they suggested the increase to 40mg (the maximum recommended dosage is 60~80mg) I think I'd go with that and give it some time.

Your doctor has the final say. My son is taking it at 40mg and it has really helped him with depression. He’s tried many antidepressants in his life. It took several months but now is good with it. I tried it but couldn’t handle the anxiety when starting it. Lost too much weight and had to switch to Mirtazapine. It all depends what you’re taking it for.