AdBlue Indicator on even after DEF Refill (P2047 & P208E)

Good day everyone,

I have a 2014 VW Passat TDI SEL. Recently my AdBlue indicator came on saying that my DEF reservoir was nearly empty, which was odd because I had recently topped it off. However, I ended up topping it off again but still ended up receiving the indicator. Then it was displaying that my DEF reservoir was completely empty and that my car wouldn't turn on again. I have been disconnecting my battery to reset the sensor so that I am able to drive my car, however every 50 miles or so the AdBlue warning light comes on again saying my DEF tank is empty (I have done this about three times already).

My check engine light came on as well (although it turned off after I topped off my DEF tank the second time) displaying the following codes: P2047 and P208E.

P2047 - SAE: Reductant Injector Bank 1 Unit 1 Circuit/Open

P208E - Reductant Injection Valve Stuck Closed, Bank 1 Unit 1

From my research on reading a few articles (there aren't many regarding this issue on this forum) my guess is that:
1.) I need to clean out the injection point as it may be clogged.
2.) My injector or the warning harness is damaged causing a false reading.
3.) I have an exhaust leak causing a false read out.

I have not performed any repairs on my vehicle as I would like to get some professional opinions before I invest money unnecessarily. Any and all advice would be greatly appreciated!