From what you describe, so long as you successfully completed the deferred adjudication probations you were placed on, these are not convictions. The charges are dismissed pursuant to completing your deferred so you've been arrested for, but not convicted of these offenses. So in short, you may say NO so long as you successfully completed the deferreds.
Because both were class C misdemeanors and if you successfully completed the deferred you can move to expunge them. Expunging them removes them from your record and they will no longer be on your record for anyone to see. this is a civil process that is somewhat complicated, so if that is something you're interested in, talk to an attorney.
Although my intent in answering this question is to aid you in the legal process, my answer does not establish an attorney-client relationship in any way. You should seek the advice and counsel of a qualified attorney in your community to evaluate your legal needs and to advise you. No Attorney-Client Relationship is created without the specific intent of both parties.
If you received deferreds on both, then you have NOT been convicted. What deferred adjudication actually means is that the adjudication of guilt (finding of guilt) has been deferred (set off). There is never a finding of guilt if the probationary period is completed (expires) without a revocation or adjudication.
Class C deferreds qualify for expunctions. You should definitely hire a lawyer to file an expunction in civil district court. This would remove both cases off your record completely.
Although I have answered the question to try to help you, you should consult with a lawyer in your area in person on the matter. In addition, my answer does not establish an attorney-client relationship between us.