Allergies to dermal fillers are uncommon. Typically it is fine to have a filler treatment despite being allergic to other medications. It is always best to discuss the situation with your injector prior to treatment.
Thank you for sharing your experience and photo. Filler migration is a possibility, but it typically occurs soon after the injection rather than months later. Given the timeline of your treatments, it is unlikely that the lines you're noticing are due to filler migration from injections...
You can consider filler to improve the shape of your lips even if you had issues with your previous filler treatment results. Two months between having the filler dissolved and the next treatment is ample time. See an expert injector to discuss your concerns.