Yes, certainly. It's also possible to sue your doctor for failure to warn about these side effects. The key is to show that you do have these effects, that they're lasting and resulting in a significant impact on the quality of your life, and that they're actually associated with the drug itself. It's a matter of proof, and you can bet that the other side that you're suing will have a team of lawyers that will dispute everything. They'll try to say that your issues are unrelated, or that you were informed, etc... so you'd have to overcome any of those objections.
That being said, you need to contact an attorney in your area that deals with product liability (specifically prescription drug) cases. Go to www.lawyers.com or www.legalmatch.com to find an attorney in your area. You should be able to find one that will give you a free initial consultation and better advise you of your rights, any problems with your case, likelihood of success, how courts are treating cases such as yours in your area, and what you should do next.
While you could file such a case "pro se" (without an attorney), it would be meaningless to do so. Again, this is a highly technical matter, and experts would be needed to be hired, vetted, put on the stand, etc... and the other side will be trying everything to get the case knocked out on any technicality. You'd almost certainly lose if you brought this case. But a lawyer would give you a much better chance of winning.
Note that what you win depends upon what could be proved. If you're older, live alone, don't have any lost wages or other quantifiable damages from this, that might result in a much lower payout than if you're young, married, with children, high wage earner that was affected by this drug, etc... Damages that can be proven go a long way to establishing a strong case.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Thank you, ***** ***** luck to you!