My husband has a judgment against him in Texas, our joined account has been frozen. I opened a new account in a different bank under my name only. Because we are married if my account in jeopardy of being frozen even though I am the sole owner of the account?

Texas is a community property state, and in most such states, a spouse's account can be frozen too, even if you had nothing to do with the debt. However, Texas has debt laws different from other states.
'...while Texas is a community property state, creditors cannot garnish your account for your spouse's debt if you did not share the account with your spouse. That means your account is protected so long as your spouse doesn't make contributions into the account or take withdrawals from it.'

from nolo.com
Bank Levies on Joint Accounts (Spouse) | Nolo.com (http://www.nolo.com/legal-encyclopedia/bank-levies-joint-accounts-spouse.html)

... our joined account has been frozen. ... Because we are married if my account in jeopardy of being frozen even though I am the sole owner of the account?

You are contradicting yourself. Twice.
1. If it was "frozen", why do you ask if it is "in jeopardy of being frozen"? It appears that it already is "frozen" (i.e.: the account has been levied upon).
2. If it is "joined" (sic), or a joint account, you are not the sole owner. Also, as Joypulv points out, since Texas is a community property state, chances are that it is in effect a joint account in any event.

The OP clearly states that she opened a second account in her name only, at a different bank, once their joint account was "frozen."

.....and Texas is an exception to the community property laws in regard to certain debt.