OP, I could have almost written your post myself. My symptoms started in January, so it's been 7 months now, though I didn't feel quite right for about 2 months before that (after a tummy bug, interestingly).
It started with knee pain (not unusual as I have had a knee injury and 2 operations in my teens/early 20s, but other knee had always been fine - I'm 38 now and really haven't had problems with my 'bad' knee for nearly 20 years).
Then about a month or two after that, I woke up in the middle of the night with a pain in my toe and swelling. I could barely walk by morning. I had to sit at work with a bag of peas on it. I thought I'd broken it, but had no memory of doing anything. It became a running joke as I'd had a few glasses of prosecco that weekend (and by a few, I mean quite a few) and even my daughter joked that I must have gotten drunk and fallen down and broken my toe. (I wasn't drunk! And I definitely didn't fall down and break anything, but it made me think I was crazy and couldn't remember some catastrophic injury I'd caused myself). I could barely walk for about 4 days and then struggled for about the next month. Toe was swollen and I couldn't wear my usual shoes for several weeks.
Then both feet/all toes started to ache along with knees. Getting up in the morning and getting down the stairs was agony. Sitting for long periods became hard. I would have to work standing up as it was just really painful if I stayed sitting. I still thought I must have somehow injured myself? Maybe because I'd recently gone back to work from mat leave and was more sedentary not chasing after a toddler, that my joints were just getting old and achy.
Then one day on the train to work, I literally watched the middle joint of one of my fingers swell up and become so painful I couldn't move it. It happened literally before my eyes in about 5 minutes. I couldn't bend that finger for probably 5 days.
Then the pain became in my feet, knees, hands, also have some costochondroitis like sterum pain. It's constant, every day, symmetrical. Some days are better then others. Some days are awful.
I also had bone breaking levels of fatigue. I've always been a morning person. Always survived on little sleep. I literally couldn't get out of bed some days. I couldn't walk up the stairs some days, I was literally so exhausted.
And oddly, recurring conjunctivities. My eyes regularly get very blood shot and I wake up with them crusted over. It's not all the time. But once a month maybe, I had a bad bout of it.
I do have some bladder incontinence, but I think that's due to a weak pelvic floor after having 2 dc. It certainly pre-dates this by several years, so I don't necessarily think it's related.
I've had all the blood tests and had x-rays. Everything came back normal, except my vitamin d was low - low, not deficient. I have been taking high dose vitamin d for the past 2 months (8000 IUs a day). The vitamin d has helped with the fatigue actually. I feel much less exhausted. Youngest dc has also been sleeping better, so that may have something to do with it too. Thyroid fine, CRP, ESR both fine. Iron levels are great.
Psoriatic arthritis has been mentioned as a possibility as well (I meet all the PEST criteria anyway). But GP was a bit like, well, just see how you feel. I don't feel in any less pain, even if the fatigue is slightly better. So I'm going back to see the GP in the next month or so (no appts until end of August though 
) to push for a referral to a rheumatologist. There has to be an explanation for this.
Interestingly, I did have several years of bad fatigue and pain in my hands/wrists (not in feet or knees or elsewhere) in my early 20s. Did all the same investigations, nothing came up. It was called fibromyalgia. I took a tricyclic antidepressant and gabapentin for about 3 years. Tricyclic did seem to help with my sleep and fatigue. Eventually I felt better and got fed up of the meds and stopped them. I've been fine ever since until now. I'm sure whatever it is is connected to that, but I'm not convinced it's fibromyalgia.