I could have written your post 2 years ago...in fact I think I did write something similar.
Some babies are trickier, they don't sleep easily or for long periods, don't lie happily in their pram/on their playmat and are just more 'angsty'. This makes your job a lot harder but it will get better.
Do try using a sling (I found the moby wrap sling comfy), at least it leaves your hands free and you might find your baby sleeps easier in it. The crying/grumpiness could be tiredness (at 14 weeks your baby probably needs to nap frequently, every hour or two). The sling won't give you a break but if it stops the crying that's something at least.
Personally I persevered with the dummy and it helped a lot with sleep in the long run, at least dp could get up in the night to put the dummy back in whereas only I could bf. Dd would only take the old fashioned 'cherry' dummies though. I used to keep popping it in dd's mouth while jiggling her in the sling until she fell asleep. Didn't always work but did sometimes.
You might find once you wean, introduce formula and solids, things improve, some babies thrive on routine and a day structured around regular mealtimes rather than feeding ad hoc (mine did). You'll get a feel for what's right for your baby, don't be afraid to try different options if one method doesn't seem to suit your baby.
Get as much help as you can afford if you've no family nearby. I used a maternity nurse one day a week and it really helped (if only to show me my baby was an 'unusual' sleeper and it wasn't my poor parenting).
Hang in there, it does get better, some babies are just frustrated at not being able move/talk and turn into fantastic toddlers.