Will it hurt my case if I work part time while applying for disability?

This is not an easy question to answer. 

The legal answer is that you are entitled to part time work if it is not considered "substantial gainful employment". You should understand that you will probably be going before an administrative law judge who must determine if you are capable of performing substantial gainful employment. Different judges look at this differently. If you are earning close to the maximum amount allowed per month many judges feel you could probably do a little more and make "substantial gainful employment". this is a personal decision you will have to make. My advice is not to work over 20 hours a week and don't make over $500.00 or $600.00 a month. Even at this level there will be a few judges that may use your part time employment against you, but those judges would probably find some other reason to rule against you had you not worked part time