Should I walk away from the first property or try to raise private money to make both deals happen? 

., you might be cutting it way too close to really do anything. 15k is the bare minimum I suggest for reserves or oh no money on any project so that doesn't leave you a ton left to work with.As @Glenn Banks said, 203k is probably your best option because it's an FHA loan and you can do low money down and the reno is baked in, but the reno is complicated.

I don’t have the money to begin something like BRRRR, but want to get into the game. 

@Paige SeeleyThe more you put down the less you will pay in interestQuestion we ask ourselves is what do you do with that money?

Find your local Private/Hard Money lenders and partner with them.

If there happens to be such a law demand the money be placed in a high yield bank account where you get 100% of the interest.

Even Do Hard Money that advertised 100% 100% you had to spend 3k on their training materials up front and spend 600.00 per loan submission.. so you needed up front money and also have to advance on the draws..

And oops, all your money is gone because it was actually a bad deal in the first place. 

My partner and I used hard money to buy property and have about 180k in house so far.

Hard money is something too scary for me to even consider.