It sounds like you want to and need to sell and therefore, a short sale may be your only option if the property is worth less than what you owe.
Was the bank even willing to do a short sale? And to answer your question about your credit - it depends. Your situation is a little more complicated because if you sold the rental for $190,000, you would be able to pay off your 1st mortgage but also have the HELOC on your primary residence.
I strongly urge you to contact a Realtor who can guide you to a person who is a short sale specialist. There are several things you would need to do and between your Realtor and the short sale specialist, they can best guide you.
I understand you don't want to deal with the property any more but perhaps using a Realtor or property management company in the short term would be able to ease the financial burdens you're facing by getting the other unit rented ASAP. You can still work to get it sold but in the meanwhile, you have tenants.