Why do I have red patches under my neck? (Photo)

You should see your laser hair removal physician in person for proper follow-up.  Skin can often get irritated following laser hair removal or it can get irritated if you shaved the area prior to your treatment.  It's hard to tell from the picture, but it looks like a simple rash, perhaps brought on by ingrown hair following your treatment?  This can be a normal reaction, but just to be safe, see your physician in person.  Good luck, Doc Halliday