Hi - she does need a bigger tank with more enrichment in it to avoid stress and boredom. 'Enrichment' is the key word with hammies and it includes - as much floor space in a cage as possible, as deep bedding as possible, a wheel that is big enough to run in with a straight back, something to chew on for their teeth. A stone or ceramic tile or similar under food or water bottle, to help keep their nails short, and plenty of nesting material (safest is torn up white toilet paper into strips) to build a good sized nest with.
I know the log with the wheel you mentioned - unfortunately that wheel is so tiny it's even too small for dwarf hamsters I think.
Syrian hamsters need an 11" to 12" wheel to run with a straight back. The 11" wodent wheel is an ideal size and is quite a slim and compact wheel. It costs about $15 I think.
A ball isn't a substitute for a wheel and neither is out of cage time (although it's good for them to have out of cage time). They need a lot of exercise and will run in a wheel all night sometimes. They love their wheels as well, but a small wheel will cause back pain so they won't use it.
For now, what you need is a bigger tank and an 11" wodent wheel, fill it with plenty of substrate so your hamster can tunnel a bit, and a big mound of torn up sheets of white toilet paper. An upturned shoe box for a house would do, with a door cut out, for a nice dark hide to build a nest in, and the current toys and chews you have.
If you can't afford a new tank just now, some people make bin cages. The samla bin from Ikea is very cheap, but it does need a bit of diy - large pieces cutting out and meshing, for ventilation.
A bigger tank is the best option - an add on doesn't give the extra floorspace. As for the bottle, some people use industrial velcro and just stick the bottle to the side of the tank
It's good that she has those wood toys and cage contents you mentioned. When do you go off to college? Definitely get the wheel asap! The cheapest place I've seen them advertised in the US is in the link below, if you can order online (or get someone else to do it maybe). And she will love it as well.
Wodent Wheel 11 inch - Wodent Wheels
Full height on the stand is about 12.3" - will it fit in your tank heightwise?
If you can get a bigger tank then a 40 gallon is the one most US members recommend. Minimum is 30 gallon really. A 20 gallon is too small. You will find her behaviour will be much more natural with more space and it could extend her lifespan as it will reduce stress.
This is the Samla bin I mentioned. This is just about big enough to be a suitable size, but anything smaller wouldn't be good.
SAMLA Box - IKEA
It costs just under $15. Most people cut out the panel in the top and mesh it, just leaving the rim. And also cut out a fair sized panel on the front and mesh that. 1cm square mesh can be held on with plastic cable ties. The downside is I think it's tricky cutting the holes in the plastic bin (I believe people use a hot knife technique).
It would work out much cheaper than a new tank though, unless you can find one second hand or in a $ a gallon sale.
Here are some great examples of bin cages!
https://www.google.co.uk/search?q=Bi...xsDbIQ_AUIBigB
Personally I think a bigger tank would be the better option at her age as she is used to it, so it would be less of a change, just the same but with more space.