I have mold in apartment and have told management for a month now and they keep putting off fixing the problem. Can I break my lease?

There are different ways leases are broken by management -- usually involving safety or habitability.  There are also ways to fix this: a) you take care of it and charge them; b) take it out of your lease to fix and c) leave.  That being said, the third option is such that you may need to seek the advice of a third party because if the "mold" is not mold or a judge doesn't for some reason believe it is an issue of habilitity, your case of constructive eviction may fail.

So, try the following:

a) www.attorneypages.com and/or

b) http://www.oag.state.tx.us/consumer/tenants.shtml