"But you must continue in the things which you have learned and been assured of, knowing from whom you have learned them"
refers in part to the "new revelation" Paul shared with Timothy, his son in the faith, so no, the OT (Tanakh) was not the only Scripture in Paul's day, and the word Scripture(s) in 2 Timothy 3:16 is not a reference to only the OT scriptures. In fact, the Apostle Peter referred to Paul's letters as Scripture:
". . . just as also our beloved brother Paul, according to the wisdom given him, wrote to you, as also in all his letters, speaking in them of these things, in which are some things hard to understand, which the untaught and unstable distort, as they do also the rest of the Scriptures, to their own destruction" (2 Peter 3:17).
Yes, the OT was important in Tim's training in the faith, since "the testimony of Jesus is the spirit of prophecy" (Revelation 19:10), from Genesis to Chronicles (the OT's first and last books, according to Hebrew order of the books), and every book in between.
The new revelation Paul received from his conversion onward was also the word of the Lord, and I'm sure Paul shared it with Tim on many occasions and in many ways (via both walk and talk). I guess you could say the words of the apostles, of whom Paul was one, were the New Covenant's version of "the word of the LORD" in the same sense the words of the prophets of old were the word of the Lord and were often prefaced over and over again with "Thus saith the LORD."
In fact, in the nascent church throughout the Near Middle East and beyond, one of the gifts of the Holy Spirit was prophecy (Acts 19:6; 21:9; 1 Corinthians 12:10; 14:5; Ephesians 4:11; Romans 12:6; 1 Peter 4:11).
While the revelation of God is now complete, as to the written word, and there is therefore no more new revelation today which can be shoe-horned into the completed canon of Scripture, Holy-Spirit-gifted men and women today can, however, speak prophetically in the sense they can speak forth the word of the Lord to each generation in powerfully convicting ways. In fact, the message of repentance can be quite prophetic in nature today, though not in the predictive sense concerning, for example, the day and date of Jesus' return. Many "prophets" have learned this lesson the hard way, even in recent months!
Is the Lord's return imminent? Yes. All we can say with any authority, however, is that it is more imminent today than it was in Paul's day!