What you are experiencing is completely normal, not only are you new to psych, you are new to nursing, period. You are going to do everything slow, people are going to get things done quicker than you, leave before you, but you'll get the hang of it. Sounds like you have great coworkers with you, don't be afraid to ask for a little help. And give yourself a break, expect that you will not be an expert right away.
My advice? Think back on your first days, what gave you the most trouble (besides the fax/copier lol) and what kept you "off your game?" Mine was always PRN meds. I'd go out in the morning and pass meds, do my assessments, sit down to chart, and 10 minutes later, someone wants a PRN, then the next person wants a PRN, and the next. I felt like all I did was pass PRN meds all day. So before I gave meds, I wrote down what PRNs they had and when they could have them. Then any that were avail, I had with me when I passed meds (cause who doesn't want their prn anxiety or pain med, and you could always return them to the pixis) and I told them when their other PRN meds were avail, that way they didn't bother you for it, at least until it was close to due.
Keep a little cheat sheet and when you are talking to them, write down things you need to chart so you don't forget. The hardest thing for me to realize was I didn't have to chart right away. That's one of the most time consuming things. I didn't what I needed to do, and charted when I had time. As long as you keep little notes, you'll be fine, especially times. I had a "brain" sheet because dealing with 8 or 9 patients, it all starts to blend in by the end of the day.
Also, I learned my best friend was my unit secretary. They always know what when where, because they are the heart of the unit. The psych techs are very important as well. They can be your best friend or your enemy. Hopefully you have some strong techs who can handle things on their own and know when to include a nurse, and more importantly, don't start problems.
Bottom line is, you seem like you still like psych nursing very much, so just give it time. Be easy on yourself. The biggest worry I would have is manipulative patients who know you're new trying to take advantage of you. Seek guidance for that. Techs are your eyes and ears, and you always you're your other coworkers. Take their advice, learn from them, and you'll be a pro in no time.