However, medicine was a big draw to my humanitarian side and would provide me with some job security. 

I have experience on both sides of the river (North and North East).

One important item of a good answer would be knowing your goals  If the answer of yours is that these are on a short term investment I would tell you to sell both units if it is a hot area and is a sellers market there I would probably say to sell both of them as soon as possible if the seller's market continues and I might not spend your own or borrowed money before you sale.  

Or simply use your cell phone hot spot.

The property is a duplex and the basement is unfinished on one side and partially finished on the other side.

All of this is still within the free interface of podio, i have been using it for nearly 2 years now with being a realtor and have added over 10,000 contacts to my CRM workspace i created in podio...One of the main reasons i played with podio lastnight in regards to tracking my rentals over excel, was i dont know how you can add receipts and documents to excel so you can track papers per property....This is a feature i have been using heavily with the podio app on my phone lately, i have been uploading the documents when a client makes an offer to the CRM, which stores them to an organized google drive, as well on my realtor expenses side i have been using it to store all my receipts and random pictures i need to store in regards to my realtor business.. these get tagged with a date and time and i dont have to go searching for them on my google drive. 

Is it possible to find any positive cash flow properties in LA during this hot market?

you can do one of several things. you can include electric in the rent (not always a good option) , you can stipulate, in the lease, that the electric bill is split 50-50, you can implement RUBS which divides the bill into the percentage of space it takes up (for example one side is bigger so they pay 60% of the electric, or the 2 bedroom pays 66% and the 1 bedroom pays 33%), or you can submeter the electric which allows you to split the bill you receive according to the actual electric used, finally you can discuss with your electric company what needs to be done to add a separate meter to the duplex. submeter and second meter are most expensive options, but in my opinion are the best for your long term sanity and profit.

@Morgan Hoke the DFW market is very hot - and has been for quite some time.

There are sections on the northwest side that experienced property managers won't touch.