Basically, this is correct, with some provisos. azə̄m is Old (Gathic) Avestan; in Young Avestan you would have azəm (with short ə), but if you use the former then the whole phrase would need to be OAv, hence with vaēnā or vaēnāmī (both with long final vowel). If you want to have it in YAv the verb would be vaēnāmi (as in the body of your question, not vaēnami as in your title).
A different question is whether this is stylistically adequate. In Avestan, as in other “pro-drop” languages, you would not normally use the nominative pronoun (here azə̄m or azəm) with a verb in the 1st person singular, unless it is specially emphasized. For the 2nd person singular pronoun you would normally use not the stressed pronoun θβąm, but the enclitic θβā. So the whole phrase would be (assuming YAv) θβā vaēnāmi.