Can sun tan and sun burnt cause night sweats?

No, not really: Adjust your room temperature down a bit.It might help if it is due to the temp in your house.

No, but you could: have hot, inflammed skin after sunburning, and that could make you feel hot. Night sweats are altogether different, and usually related to hormones, thyroid dysfunction, etc. So, check with your doctor if this persists for more than a few days, especially since you say you have a lump at front of your neck (thyroid is located there!)

Possible: If hot, and dry, your body may be trying to bring temp down.