Hello and welcome to BW forums
It's quite normal at 8 wks old that your LO just wants some company and to be held, I wouldn't worry too much about this being a sign of a "clingy baby" or what the future holds in terms of ability to play independently.
Refluxers quite often need to be more upright and even an elevated chair/basket etc may not be enough of an angle to actually reduce the pain or discomfort of the acid. if she is experiencing acid coming up then she may need to be more upright and the way she gets this is to cry for attention and stop when she is lifted.
I also found with my refluxer he absolutely hated a bouncy chair I got him. I though it would help as it was elevated but he would initially look quite happy for about 1 min then scream blue murder to get out of it. We got very very little use out of it before I totally gave up - it just was not a comfortable place for him - he did better on the floor to be honest.
Gaviscon is a common medication for a first try. Mine also started on gavi. Many people here have found that gavi shows initial improvement but doesn't seem to last so after a couple of weeks the symptoms are all back and it's just not working well enough. I would keep this in mind as your DD might need to trial a different medication to control the acid.
Also if/when the gavi doesn't work you will likely experience all the same problem you were having before including disturbed sleep, nap problems are not always about routine or LOs ability to self settle.
Another aspect of reflux many of us have experienced is that LO might feed better at night than they do in the day and might not need to be elevated for 20-30 mins at the BT feed, the dream feed or any night feeds. You might experiment with this and see how it goes because it can make quite a big difference to everyone's amount of sleep if you can pop LO back in the cot after a night feed rather than holding for the 30 mins.
Just going back to your worry about clinginess.
All children experience phases of SA (seperation anxiety) which is an absolutely normal developmental phase. It is often linked to certain developments (such as learning to crawl and learning to walk) but can also be caused by changes in their life and routine or pain (reflux, teething, illness). It's amazing how they tend to know when they need more attention and when they can mange quite well with less.
At 2 months old your LO is still bonding with you, the ability to bond and have physical contact with you is absolutely essential for healthy development so your baby will seek this out - even if it means complaining whilst you try to put her down for 5 mins so you can shower!
If you have already started naps and night sleep in the cot (well done!) your LO will already be spending more than half her time not being held - it makes sense she wants as much of you as she can get during the time she is awake. She is probably now starting to show more interest in the world around her too, so she will be looking to you for your smiles, songs, chatter, and to introduce her to the world in those short periods she is awake between naps.
Generally the advice with bouts of SA for older LOs is to take LO everywhere you possibly can with you and to put aside any non-essential chores for a few days until the worst of the phase passes. Often the phase will pass more quickly if you give LO the attention and reassurance they need rather than trying to get them to used to being alone - in effect you spend more time with them, more picking up and more cuddling, touching and talking which fills their need, increases their confidence and they will then be ready to take steps into the big world independently, knowing you are always there to return to for support any time needed - you are the secure base from where they set out and return after their explorations. if you try to push a LO away to encourage independence the chances are it will back fire and they will be ever more clingy and unwilling to make those steps into the big world.
Obviously I can't say what your cousin did or didn't do, and I don't want to judge, every parent does their best for their child and does what they believe is right, every child is an individual and some are more "clingy" than others depending on their character and temperament. I would just say to you that knowing someone with a "clingy" child doesn't mean that your child will be the same or that this is something to worry yourself over. Try to focus on the bond you have with your baby and teaching her that you will always always be there for her, no matter what...this is really the only thing you can do if there is anything that can "avoid" having LO become clingy.
I hope this helps.