I don't have much more experience than you but I was in the same exact position (in peds too :) ). Here is what has changed and helped (though I'm still the one who never sits down...). Some of these may seem really stupid, I had no clinical experience prior to my job and had a preceptor with tons of experience who didn't need brain sheets, etc to make it through her day!
Brain sheet - used well. For example, when I had hourly I/Os I'd always be checking to see which hours I had charted. It took me 4 months to realize that if just crossed that hour off of my brain sheet I wouldn't have to go back into the electronic chart to check. Duh. So now as I chart I "x" out that hour on my sheet. I'll still glance at the end of a shift to make sure I didn't skip an hour by mistake but not double and triple checking all that charting helps. Same thing for all the other random charting - I have 4 letters (Q, A, P, N) for the hospital specific charting that is required each shift - pt classification, assessment, nursing note, nutrition assessment. I cross them off as I do them - again, I spent a lot of time checking "did I actually write the assessment for this kiddo...?".
Getting better at chunking care. I used to always forget to bring the 10AM meds in with the 9 AM meds... I was so "in the moment" I didn't look ahead. Got a baby who has PO meds? Try to give them with feeds - 10ml of formula in a bottle with the meds and then the rest of the feed. If its something like a vitamin and the admin time is flexible don't go in twice - chart it as not on time because it was given with meal/feed.
Do you have computers in the rooms? Sometimes doing a daily assessment while you are in the pt room helps because then when you realize they looked like they had increased WOB with subcostal retractions and accessory muscle use but you can't remember if they actually had nasal flaring you don't need to walk back in to check.
Delegate. Its ok. Don't sit on your ass looking at FB on your phone and delegate - but if you need to chart or see another pt - delegate - its ok. When you get better and have some free time help the assistant staff out - offer to do vitals, get equipment, etc - do so.
Don't double chart. If you put in a long note mid shift about something, don't say the whole story again for an end of shift note. Say "see previous nursing note" for the details.
Eventually you will just get faster at things too. You'll begin to learn meds and their appropriate doses and infusion times and what IV fluids are compatible with what meds and you won't need to check all the time.
Just keep plugging away!