My DD2 is 17 weeks and exactly the same, though she will now sit for periods of time in a bouncer, I think that's because as I have DD1 she has had to sit and cry every now and then (eg whrn DD1 needs food/toilet) as much as I hate it!
I have tried formula once a day, she is more settled but it just buys me time, the screaming and inability to sleep isn't helped sorry!
I have also been advised to start adding solids by my HV as she is showing signs (alert, chewing hands etc).
A caveat here before I get jumped on! I followed guidelines for DD1 she was 6 months, but I for once have a massive amount of respect for this HV, she has looked at the research backing the WHO and most is in developing countries where babies over 6 months survival rate from cholera etc is better so avoiding anything but breast until then is best. 65% of Europe and the US do not support waiting until 6 months. Current thinking apparently according to the research/seminars she's been doing is that between 17-22 weeks there is a weaning window where it can be introduced baby led. And in fact waiting until past 6 months is leading to an increase in feeding difficulties.
She seems to make sense, we feed baby on-demand, co-sleeping will result in a better sleep (though I daren't do it, a point we have argued over as she's a firm believer I won't squish her!), so why not give the baby solids when it feels natural? A little taste of appropriate food, if they want it they will eat, of not they won't. True baby led weaning not spoon feeding at an exact time!
She then mentioned in humans natural state we gave per-chewed food when mum felt baby was ready which helped digestion and immune system but I draw the line there!
Anyway long post it's totally up to you but I just wanted to pass on the information I have about guidelines and that I intend to offer my DD some baby rice and a spoon and we could end up
A- content non hungry baby
B - a baby who is weaned and still unsettled (look at Hugh needs baby, that's what I was directed to)
C - an unholy mess with no consumed food telling me she isn't ready :)