M.P.
I don't know what you mean by the term shelter her. It is a parents job to shelter their children based on their needs at each age. It is reasonable for her to act the way she did at her first visit with "strangers" and it's reasonable that this was her first visit.
I would do the next visit differently. First, I'd be sure she had napped and eaten if it's at the time she usually eats before taking her to your friend's home. Her cries at each time sound to me the result of feeling unsure about what is going on. I suggest keeping her with you anytime she seems about to cry. Not necessarily pick her up but sit down beside her, pat her back, give her a hug, anything that let's her know in an active way that you are there before she breaks into full scale crying.
If she starts to breakdown a second time, I would suggest picking her up and holding her, again before the crying begins. And then shelter her by not introducing anything new to her. Going into a darkened room with her is a good idea. I'd be careful about nursing her to quiet her because she may then associate nursing as the only way to calm down after non-food issues. If she's crying because she's hungry then definitately nurse her. If she's hungry or it's near the time she usually nurses then nurse her before you put her in a new situation.
Your daughter is just reacting to being in an unfamiliar situation. I suspect that she was overwhelmed during this visit because there was more than one new thing happening.
I think it's OK that she hasn't been out and about at 4 months. That could be called sheltering which I think is a good thing. She is in a new world, her nervous and physical systems are newly developing. You don't want to overload her. Babies are not small children and small children are not adults. As we age we become more able to adapt to new situations. Even as adults we continue to mature into more advanced stages of interaction with the world. I'm 65 and I am sometimes still not comfortable with something new that requires my interaction.
Gradually introduce her to new situations. You wrote that she was fine at first. I suggest that you arrange for more visits that are shorter in length so that she can gradually get used to being with other people in different environments.