Regardless of the type of graft material that was used (freeze dried, bovine, artificial), they are all sterile and generally non-allergenic. Theoretically, an individual can be allergic to anything that is considered a foreign body. However, it would be very unlikely that you would have a reaction to the bone graft material or membrane (if one was used) as these are made from materials that naturally occur in the body. The more probable explanation is a reaction to latex gloves or something else that contacted your lips/face (powder, ointment, surgical drapes or ice packs). If it is improving, it will continue to do so and no treatment is needed. If it remains the same or gets worse, you should see your dentist and he/she may recommend topical steroids.
The edges of the Invisalign tray are often irregular or jagged and can cause the irritation that you describe. Your dentist/orthodontist can easily smooth and polish the edge, but in the meantime an emory board or nail file can be used to soften the edge at home until you are able to see your dentist.
If the next tray in the series fits (albeit tight) and seats completely on the teeth, you should be able to move ahead. However, I would recommend consulting with your dentist/orthodontist as well. If they feel the teeth are not tracking well (fitting within the next aligner) a replacement aligner can be ordered from Invisalign.