Is it possible to tell the difference between a young star that is just "big" and an older red giant? I read the Wikipedia page for one of the biggest known stars, UY Scuti, and was curious to see the age of the star isn't really known at all.
When a star's hydrogen fuel is exhausted, it starts burning up helium and expands into a red giant. UY Scuti is defined as a red hypergiant/supergiant, but if we don't know the age of the star, is it purely a guess whether it is just a big star or one which has exhausted its hydrogen and expanded into a red giant?
Are there upper limits which predict the largest size new stars can be created?
 A: There are four classes of red giant, with different properties.
Three are produced by low(ish) mass stars (1-8 solar masses) and in order of evolutionary phase:

*

*There are red giants that are burning hydrogen in a shell around an inert helium core.


*There are red giants with helium burning cores, called red clump stars.


*There are then red giants that are burning hydrogen and helium
shells around an inert carbon and oxygen core. These are known as asymptotic giant branch (AGB) stars.
The fourth type are higher mass stars that are undergoing significant shell-burning of hydrogen, helium, or even heavier fuels, on their way towards a core collapse supernova. These are the biggest of the red giants and UY Scuti is one of these.
The common characteristic of all these red giant types is that as well as being large and cool they have exhausted hydrogen in their cores and are burning nuclear fuel in a shell or shells around the core.
It is difficult to precisely know the mass of AGB stars or the red supergiants. Not least because they are actively losing lots of mass. AGB  and red supergiant stars with a range of masses have quite similar observational properties. If the mass is unknown then so too will be the age, because the mass of the star determines the age it will be as it goes through each of its various evolutionary phases.
There are better possibilities to estimate the masses and therefore ages of red giants and red clump stars via their pulsations and asteroseismology.
I am not sure what you mean by "a star that is just big." A massive young star is big, but it is also going to be much hotter than a red giant. The only way a star can look like a red giant is if it is large and cool.
It is possible for very young protostars to be large (though not really as large as something like UY Scuti) and cool for a very brief phase (<1 million years, so they would be rare) of their early lives as they contract towards the main sequence. We would not call these red giants. You can (usually) tell the difference between a protostar and a red giant from their immediate environment. Protostars would normally be found in young clusters and star-forming regions and are often surrounded by an accretion disk and might even be embedded in an accreting envelope. Beyond that it is quite difficult from an external observation to work our whether a large, cool object has the interior structure characteristic of a red giant unless one has access to asteroseismology data.
Edit:
A further way to tell the difference between a red giant an a young protostar would be to look at the photospheric lithium content. The red giant will have evolved from a star, probably more massive than the Sun. Such stars will normally destroy their interior lithium in $p, \alpha$ reactions. When the star become a red giant, the Li-depleted material is mixed to the surface and the observed photospheric Li abundance (using the Li 670.8 nm line) would be very low. In a protostar, all the original Li is still present because the interior is not hot enough to burn Li.
A: Yes, a young star that is just big (very massive and dense) is far hotter than a red giant (big in extent & massive,  but not dense) and so has a distinctly different light spectrum. By measuring that spectrum through a telescope, along with its apparent brightness and redshift distance, we can easily tell young, blue supergiants from red giants.
A: Yes. The spectrum of emitted light is different, in both the thermal radiation and the spectra of the elements present.
