Maybe some others can chime in too about how long it takes for meds to kick in. Usually for me by 4 weeks I feel more normal. It is such an individual thing, though.
Wow, yeah being a nanny requires a lot of energy and dedication, esp. since you are engaging with the child(ren). It's great that your mom can take ds for a night on the weekend. You *need* a break!
I hear you on getting stressed while you're trying to get something done and your ds is constantly vying for your attention. I really hear you. It's hard to know where the line is - how much do you ask your child to wait? how much do you continue on your task? when do you interrupt your task? etc.
I too get my buttons pushed and find myself struggling with frustrations over trying to get something(s) done and juggling that with being present for the children. There have been a couple of books that have been helpful, and counselling has been somewhat helpful. But when the meds aren't working then I can't apply the things I've learned well enough because my mood is so overwhelming.
What meds have I tried? When I was 17 - Luvox. Not a good fit for me, but it's my MIL's favourite.

In my 20s Effexor - not great for me, but commonly used and good for some. Up to that point the side effects were always so unbearable that I was not able to take more than one pill of either med. !!!! I had really bad depression and anxiety after dd1 was born (traumatic birth, childhood traumas resurfacing, rage issues, it was horrible) and it went up and down. When things were better I got PG with dd2 and felt depressed again. That was when I went for meds - I was desperate and willing to try anything. My whole life I had tried to manage my mood with lots of exercise, supplements/vitamins, good food, journalling, talking with friends, counselling, trying to get enough sleep, cognitive behavioural retraining skills, etc. But once dd1 was born, that was NOT ENOUGH anymore. Looking back it was somewhat helpful some of the time (before kids)... but not a cure-all.
I found a psychiatrist who was willing to start me on a super duper low dose of Prozac and slowly incrementally increase the dose so the side effects were manageable, and I was able to function in my life (keep going to work and take care of my children). In the end we added Wellbutrin too, as I find the Prozac is really good for anxiety and helps relax me, but the Wellbutrin energizes me and helps with the depression part.
Lately I feel like my meds are not working as well as they used to so I will see my pdoc on Tuesday... and we'll talk...she'll probably up my meds again.
Anyway, I hope you get a session with your counsellor soon. Do you know anyone in real life who has been on meds?