Hi domestic I also have a 16 week old, and am finding the same. DD is often more interested in tv/passers-by/DS/DH than feeding during the day, but feeds without interruption in the night, or if in a quiet room. I think she's at that age where they're starting to discover the world around them!
Crying - I'm sorry you're crying and feeling down about it - you're doing a fantastic job having made it to 16 weeks already. I couldn't make it past 3 with my first DC, and I felt like a terrible failure for having to switch to bottle feeding. I know it's hard, and can be frustrating. Is there a BF group or surestart centre you can pop into, and speak to someone about how you're feeling? If all else fails, speak to your GP. You have every right to cry and feel frustrated about this all but you'll get through it, one way or another 
Now for the feeding!
Have you tried taking a shawl or a big cardi out with you and draping over your shoulder/her head when out, so she can't see anything stimulating?
Also, can you find a cafe where you can sit comfortably in a corner, and relax. It may sound obvious but if you're tense about feeding her, that can sometimes slow your milk flow, so she'll have to work harder for her food - that could frustrate her.
Don't stress about it, if she pulls off, and looks around, just let her have a look and once she's satisfied her curiosity, she should turn back to you. There will come a point where she'll just stop - you may feel like she's not had enough, but she'll get nutrition from what she does take (she is putting on weight, so she is getting something, and putting it to good use
). If she needs to feed again in a hour, so be it.
My DD sits there, feeds fine for a few mins, then drags her head round with me still attached (ow!) then lets go or turns back. After a few looks she either knuckles down to her feed, or else gives up completely. I often find her with boob in mouth, looking at me and grinning. Once she's sat there for a few mins and not shown that she wants more, then I put it away. She soon learns that there's only so much I'll stand for!
Wait a few minutes to let her decide, and she'll either crack on or not.
The last thing you should do is stay at home - it may sound blunt (and I don't mean it to be!) but if you stay in, how will she get used to feeding when you're out and about? Of course it'll be different and more interesting than what's at home or in a quiet room! Can you go out with someone, to sit with you and chat with? It'll help you to relax too 
I wish I could meet up with you to support and compare notes! :o HTH, chin up and keep trying