As you start your Orthodontic treatment your teeth slowly adapts to the forces applied by the braces which may cause issues like broken braces or bands which are applied on the molars mainly to derive proper force from them. So during this period you may face these problems.
Next Steps
As of now it you are not able to attend to your Orthodontist immediately you can apply sticky wax the wire ending which is causing injury to your cheek. As soon as you will visit your Orthodontist they will fix this problem and your treatment will proceed as it is.
Health Tips
If this is not fixed within a week or so uneven force distribution might take place which may cause delay in treatment.
Please don't try to cut this wire forcefully by yourself you might end up hurting yourself more.