Is it normal that my lips are this bad & sore, and my skin is peeling and causing pain? (Photo)

I appreciate your concern. I don't see anything worrisome. but some bruising. I suggest you try to manage the swelling and hydrate the skin. My video link below has some tips.
Good luck. Dr. ALDO

Yes, this can be typical after lip injections. Swelling and/or bruising will last 1-2 weeks. Icing, arnica and VBeam treatments can give improvement. If you're unhappy with your final results, you can have it reversed with hyaluronidase and try a different technique next time. See an expert. Best, Dr. Emer

Yes, this can be typical after lip filler. You can have some soreness, swelling and/or bruising after injections. I would wait a full 2 weeks before judging the results. If it is after the two week wait, you can have the filler reversed with hyaluronidase.
I hope this helps!

Thank you for your question. It is normal to have some swelling, bruising and discomfort after lip augmentation with hyaluronic acid fillers such as Restylane and Juvederm and can take up to 2 weeks to resolve and see final results. You can apply cold compresses to your lips to help reduce swelling. It is also advisable to avoid NSAID’s such as ibuprofen before and after treatment as they tend to thin the blood and increase the risk of swelling and bruising. If you have any concerns it is always best to contact your injector. Best of Luck!

Many individuals experience bruising or swelling after lip fillers. Usually, these symptoms will reduce 2-3 days post injections, however if you are experiencing pain or discomfort I recommend scheduling a follow-up with the injector that preformed the treatment. In the meantime, you can apply a small amount of topical hydro-cortisone with Aquaphor at bedtime. I hope this helps! 

Yes, this can happen. Moisturize your lips, and avoid products that can cause bleeding (like Motrin, Advil, Aleeve) both before and after your injections. If things don't resolve in a week or two, I would suggest seeing your injector for additional guidance. Best of luck!