DD actually has had a few 30 and 45 minute naps too lately and we go back to pu/pd when that happens. I think it's due to overtiredness when they're nights are out of whack. I know for sure that if she has been up for 3 hours before the nap, that a 30-45 minute nap is not adequate so I do pu/pd and so far it has worked to put her back to sleep. Sometimes all she needs is 'sh' while in the crib, sometimes I have to pick her up. If she fell asleep after only 2 hours awake time and woke up babbling and happy, then she's had enough nap and pu/pd would only result in screaming bloody murder for the next hour. DD is fairly easy to read that way, that is if she needs more sleep, the whole resettling routine calms her. If she really doesn't need more sleep I could pu/pd till bedtime and it wouldn't work.
Her only taking one side at feeds is interesting. Is she on a 4-hour EASY? I'm sure the cold is a big contributor. DD just had her flu shot and that has made her feel pretty tough for the past 3 days and her food intake has definitely dropped. In general I don't worry about intake as long as she's not trying to feed at night. Following the dreamfeed my rule of thumb is no feed for 6 hours at this age, so if I DF at 11:00, the soonest I would allow BF is 5:00am. And even then I try to help her resettle first. She WILL NOT resettle and cries quite hard if it is actually hunger at that time.
As for pu/pd dd does the same thing sometimes and will settle as soon as she's picked up. I have found with her that if she cries as I'm setting her down I put her right down and try to sh/pat for a few seconds to see if she'll settle. Eventually that does work and I don't have to pick her up again. My dd's cue that she won't be settling is if she is kicking her legs. If she sounds frustrated but not kicking, she'll probably settle with more sh/pat. If she's kicking, I keep doing pu/pd, then eventually on one of the pd's with sh/pat she jsut turns her head and settles. I just try as much sh/pat as I can first before picking her up. I have found with little regressions that it only takes about 3-4 sleeps (naps and bedtimes) to correct little problems with pu/pd.
All that being said, it is pretty tough to implement anything while a baby is sick. Once she's feeling better, then you can go hard at the routine
Good luck