Would you be able to find work - yes, definitely.

This was the late 1940s, traditional gender roles were still very much in place. While the women had taken over lots of jobs previously held by men during WWII, as soon as the men got back from captivity the women often got send home again. Part of the reason was the majority of the traditional apprenticeships and master craftsmen degrees were only open to men, so many women had no formal training in their jobs while the men did.

Additionally lots of jobs at the time involved physically hard labour (farming, mining, steel work), which women struggled to do.

Would you face some sort of punishment - that really depended. Normal Wehrmacht soldiers had litte to worry about, but those in the SS, SA, the NSDAP party members...

You got to remember that Stalin was still in charge in those early years. So anything that could get you in trouble in the Soviet Union under Stalin could also get you in trouble in the GDR. Many innocent people were dragged off on trumped-up charges of "sabotage" and never seen again. Ditto for not-so innocent people. The Soviets did not care too much about a fair trial, if you looked like a nazi or if they thought you were a nazi, you had a train ticket to Siberia waiting for you.

Public would treat you like any other person. Having fought in the war was a very common experience, the youngest soldiers were 14 and 15 near the end of the war and the oldest near 50, with some men being well over 70. Pretty much all males born between 1905 and 1930 were send off to war, only those who were needed to keep things running at home were allowed to stay with their families. Having fought in WWII for males born in those years was as common as graduating high school is in the USA today. It was simply no big deal.