I'd advise talking to your doc about the side effects. There are plenty of other effective antidepressants on the market that don't cause those issues. Wellbutrin is particularly helpful for those who don't want to suffer from impaired libido. The drawback of changing meds is the delay before they take effect: most antidepressants take several weeks to work.
Long-term - well, define long-term. I have friends who've been on the same ADs for more than 10 years. My oldest sister has been on tricyclic ADs for more than 30 years, I kid you not. Two years is nothing. The long-term effect I've seen with most people is that that particular med stops being effective. I was on Serzone for more than 7 years myself before it quit working. Switching to another med corrected the problem.
Rather than going off meds altogether right now, I'd aim for finding a medication you can live with for a few years. When you can find one that allows you to gradually titrate your dosage downward without noticeable increase in your depression, then you can think about getting off the meds. Untreated depression is generally going to be more dangerous for you than most meds.
I'm off all ADs now (although I still take an anti-anxiety med), but it took me more than 25 years. I didn't become addicted or anything like that, it's that it took that long before my depression didn't recur almost immediately on stopping the drugs.
Talk to the doc. Tell them the Prozac is too speedy and it's killing your sex drive. Ask to try something else. There are dozens of other options.