Okay so if I understand you correctly you are not having any trouble with chord changes when using a pick (presumably to strum) but if you are playing fingerstyle one string at a time with a pattern or using a pick to pick out individual notes of a chord (in a pattern) - then your transitions between chords simply fall apart.
If that is what is happening the only explanation I can think of is that you have too much going on in your brain at one time trying to remember which string in the pattern to pick in which order at the same time as you are trying to remember how to switch to the next chord.
Here is the thing. Learning guitar is quite challenging on multiple levels. You have to train your brain to teach your fingers to contort into many unnatural and unrelated formations to play various chords. And you have to remember how each one goes. When you first learn a new chord sometimes you have to think "now how does that chord go?" Not easy to get your head around.
When picking a individual string pattern either with fingers or a pick, now your brain must remember a particular pattern and your muscles must learn to move your fingers to a very precise point to pluck an individual string without touching the surrounding strings. Then immediately your brain has to know what the next movement is in the pattern and you have to start focusing on hitting the next individual string etc. A great deal of mental processing taking place.
After only 6 months of playing, its not surprising that you are struggling a bit with mastering both a complicated picking hand pattern together with remembering freshly-learned still-a-little-strange chord formations. It's just too much to ask your brain to do all at one time in the beginning stages of a lifelong journey. You are having to concentrate on what to do with your right hand and what to do with your left hand and they are both doing different things at the same time and neither thing is something you can do without thinking about it - yet.
I think you need to spend more time practicing the picking patterns until you can do them without conscious thought. If you watch television or a movie at home, hold your guitar and just repeat the pattern over and over again until you can do it without consciously thinking about it.
You should have the same comfort level with your chords where you are able to play a C chord on command with no conscious thought as easily as you can make a peace sign without thinking about it (or any other type of hand signal that you may have memorized).
Once you have developed the muscle memory for both chord formations and a picking pattern to the extent that you can do both while carrying on a conversation (without conscious thought), you will have no trouble transitioning between chords while playing the picking pattern. And it will come just as easy as it is to walk and chew gum at the same time.
Just be patient and realize that mastering the guitar is a long term proposition that requires dedicated practice. And don't fret it (excuse the pun) if it takes a while to master finger picking. I have been playing guitar for longer than I care to admit and I still have not mastered finger picking. But if it's something you really want to do, given enough time and dedication - it will come. I have seen beginning guitarist pick up on fingerpicking quickly if they are intentional about practicing regularly. But 6 months is really not much time.
Have fun on your journey towards mastering the guitar.