If you are looking for good sound quality then you want a separate DAC and streamer. Both of similar quality. Typically separates sound a lot better and set you up to upgrade stepwise in the future. Yes, I would sell your DAC.
If you want a significant step up consider something like Schiit Yggdrasil DAC… this is a high quality low cost streamer that has better sound quality than you would expect for the cost. For a streamer, maybe a Lumin U2. While BlueSound streamers are most folks first streamer, I have found an equivalent quality streamer improves the sound significantly. I own Aurender streamers… they are typically at the top of the list in any category, but I am guessing they are a bit above your reach.