Dear Kate,

in the first place it is very unlikely to hurt a LCL while cycling without trauma or fall. It is more likely that you overused a tendon or bursa. Ibuprofen is not indicated at this stage, as the tissue should be out of its primary inflammation stage.
I think a good check up by a PT or physical doctor (specialised in sports/orthopaedics) is necessary. It is far more likely that you have a overuse of the tractus iliotibialis (see details about runners knee or IT band syndrome). But first you need to rule out other sources of pain, like meniscus of patellafemoral pain.

Good luck

Sietze