Could clonazepam be the reason I feel a hangover type feeling everyday?

Definitely. Clonazepam is a long-acting medication, and causes significant sedation and cognitive slowing. Depending on what it is being used for, there may be alternative treatments that would not carry these side effects.
It could. Depends on the dose and when you take it. Clonazepam is a very long acting drug, and really doesn't need to be taken more than twice a day. Some doctors prescribe it for 3-4 times a day, and then it will accumulate and potentially cause "hangover" like feelings. If you are experiencing this side effect, your doctor should reduce the dose or consider an alternative treatment for you.