Does lack of sleep increase my pain?

Yes. Lack of sleep can affect many bodily functions and may increase the stress on the body which, in turn may increase the sensation of pain. Getting a good nights sleep as well as moderate activity during the day can help decrease pain. However, sleeping too much, may make symptoms worse. Most people require on average 7-8 hours of sleep per night.
Yes. Lack of sleep may make all chronic problems worse by reducing your body's ability to deal with adversity. Sleep restores this ability. Inability to sleep needs to be addressed in all cases of chronic conditions, preferably in some way which also addresses other issues, like emotional disorders (depression, anxiety, etc).
Yes. Lack of sleep affects your pain threshold more important would be, does pain not let you sleep at night and why.?
It could . Proper sleep is a vital part of being healthy. If you sleep poorly, are sleep deprived, or do overnight shifts you have little chance of being completely healthy. Improper sleep will adversely affect your hormones, your nervous system and your immune system leading to biochemical imbalances & an inflammatory response making the inflammatory/biochemical mediated component of your pain worse.