Possibly. There are several factors you need to consider before you can bring a lawsuit.
For example, the side effects might have been discovered during clinical trials and then disclosed to you on the product packaging. Your doctor should go over the side effects with you before signing a prescription. If you were warned of the dangers, then it is much harder to bring a lawsuit because you gave your informed consent and assumed the risk of injury.
However, the side effect might have been unknown by the drug company, your doctor, or the pharmacist. In this situation, you might have a valid legal claim, especially where the drug company hid information about severe side effects.
The strongest situation is where you experience a side effect because of a defect with the drug. Most drugs have side effects, even under the best circumstances. But if your medication was contaminated or was at a higher dosage than expected, then you have a much stronger claim to compensation. You might also have a case where the instructions are confusing or inadequate, causing you to misuse the drug. Discuss your case with an experienced attorney.