Will I continue to experience side effects even after I have been cured of HIV? 

That is impossible to say at this point. Many different strategies to HIV cure are being investigated, but no one knows exactly what an HIV cure will look like. As a result, it is not yet clear what this will mean for the side effects you are currently experiencing from HIV or HIV medication.
 
If you experience significant side effects from your HIV or your anti-HIV medication, always report this to your specialist HIV doctor and nurse.

Sometimes it can help to switch to another medication. This is not always necessary. Sometimes you can counteract the side effects with other drugs. Always do this in consultation with your doctor.