Can I replace loose ball bearings with caged ball bearings in my hub? I currently have loose ball bearings for my hubs and I am wondering if I can put caged ball bearings in there instead. Can anyone let me know if they are better or worse than loose bearings. 

Also I thought of asking this because I noticed my front wheel was making quite a bit of vibration when spinning so I opened it up and added one more ball bearing to each side as there were only 9 in each side even though I surely remember taking out 10 from both sides when replacing an axle in the past. After this, the wheel would not move at all as each ball would rub on eachother so I left it with 9 balls each side, but I still don't feel right about the fact that there is some space between each ball in the hub. This is why I thought it might be a good idea to switch to caged ball bearings. Is the space between each ball a problem or am I overthinking it?
Yes, you can get caged bearings to go in the hub. RJ The Bike Guy seems to have several YouTube how-to videos (hint: they have to go the right way round)

No, they are not better than loose balls. Caged balls are spaced out evenly, but have fewer balls in total which means fewer balls sharing the load, so they are said to wear out quicker. 

With loose balls, you need to leave a little bit of room for them to move, so you’d put in one less than fills the whole cup. Given that caged sets typically have seven balls, if you put nine in loose then you’ll still have more bearings (better) than using a caged set. I.e. if you’re concerned about the space between balls, 9 loose is still preferable to 7 caged. 

Some front hubs can take 10 balls, it depends on the design. You need to figure out which size your hub requires - presumably the majority of your balls are still the original size. If you can measure that then figuring out, or asking the LBS, or asking here in another question with photos, how many to put in, should get the hub running smoothly again.