Are my Dhuhr and Asr prayers valid after combining and shortening them, while delaying the Asr prayer until the time of the Asr Adhan due to obsessive thoughts (waswas) about ablution and prayer?

Your Dhuhr prayer is undoubtedly valid. As for the Asr prayer, the majority of scholars consider it invalid due to the absence of continuous succession (muwalat), which is a condition for combining prayers by performing them early (jam' al-taqdim). However, those who do not stipulate continuous succession (like Shaykh al-Islam Ibn Taymiyyah) consider it valid. This latter opinion has strong foundations, even though the opinion of the majority is more precautionary. Since the event has already occurred, your prayer is sufficient, and you are not required to repeat it, because the act of an ordinary person is sufficient if it conforms to a recognized scholarly opinion. One must be cautious of obsessive whispering (waswasah) and not yield to it.