can the unemployment office refuse to pay me!

You question holds two possibilities for the TWC's refusal to pay unemployment benefits.  First, TWC will not pay you benefits for any period of time covered by a severance benefit or payment.  Normally TWC would tell you "you are eligible for benefits but they won't start for 2 months" representing the 2 months severance you received. "Misconduct" is also a reason for denying unemployment benefits.  Misconduct is defined on the TWC's website and it is a bit narrower than the common use of the term.  In general it requires that you violated a written policy of which you had notice or that you did something so outrageous (for example stealing cash from the register) that any common person would know constitutes misconduct. If TWC has otherwise approved your unemployment, but is waiting to pay you until the two months of severance is exhausted, I am not aware of any remedy you have.  If the TWC says you are guilty of misconduct and is denying your unemployment altogether, you may appeal the initial decision to a telephone hearing officer and, if you don't like the hearing officer's decision, appeal it to the 3 commissioners of the TWC and, if you don't like their decision, file a lawsuit appealing that decision.  You must go in that order.  You must carefully meet your appeal deadlines.  Failure to adhere to the deadlines will deprive you of your opportunities for further appeal whether or not you are right in your position. Good luck.