I have all of my data from my old macbook pro in an external hard drive. Basically it's my old Macbook hard drive with external casing. It was working fine before when retrieving files using my new macbook air, now I can't access any files?

I can't access any of my files, photos, anything form my external hard drive... It worked before now when I plug it in the light comes on, but it doesn't even show up as an external drive, so I can't access anything, I'm worried I have lost everything...

Huge mistake was only having ONE copy of your data OFF computer,
most people do it, and its just horrible and the typical reason for serious data loss.
Likely you have a very common failure (extremely common actually) called SATA bridge card failure, which would be "good" news,
read about same here:
Your dead external hard drive is likely fine! Great hope for your 'faulty' external HD
Never again let yourself have LESS than 2 copies of your important data off-computer,      ever
1. verify the external HD doesnt show up on another Mac
if same, you have about a 8 in 10 chance its SATA card failure.......... easy to fix.
The great news at the end of the tunnel of an apparently failed or failing external hard drive.
When checked on another computer, and with no need for spending money on data extraction expertise or software, the very likely case is that your external USB or thunderbolt HD is in fact fine, and merely the card interface, or SATA bridge card has failed or is failing.  Keeping a HD dock around handy, or cheaper still a $20 hard drive enclosure or a SATA to USB connector can be a real life saver in getting your drive back to use, when the drive itself is fine, and merely its interface card has gone bad.
The SATA bridge card inside a USB external HD has a very high failure rate in general
Typical SATA bridge cards as seen inside a 3.5" external HD with power input (#1), and 2.5" SATA cards (#3, #4, #5)
What are the realistic odds your HD is perfectly fine?
There are no hard facts whatsoever, especially since so many people discard their assumed “dead/faulty” hard drives, but a good educated conclusion from years of examining and seeing this issue is that for hard drives made since 2010, and not dropped or generally abused, is that a minimum of 50% conservatively are perfectly fine! I personally estimate however that it likely approaches 60%+.
Considering how many external hard drives ‘fail’ (rather the SATA bridge more than half the time) each day, that is a very high number of perfectly fine HD that are tossed!
This is especially common with 3.5” desktop HD that are connected 24/7 with power and see a lot of data transfer. People wrongly conclude that “X” mfg. just made a defective drive, when in fact their 3.5” drives inside the plastic enclosure is 100% fine.  I have personally seen well over 200 of these dead SATA cards and additionally seen 3 fail within a one hour span of doing a large data copies.
One of the very reason pros use bare HD as inserted into HD docks is not just the saving of space and the need for endless USB cables, but the elimination of the need for this high failure-rate part.
While the shapes and sizes vary somewhat on SATA bridge cards, they all serve the same purpose and have likewise failure rates
What exactly is the SATA bridge card in your external HD?
In the middle to late of 2009, most all external hard drives both in 2.5” and 3.5” reached the shelves in SATA III. These small SATA cards or "bridges" are used to translate between the hard drives’ interfaces and the enclosures' external ports (USB, Thunderbolt, Firewire). Additionally these small bridges not only transfer power but also of course the data. Unfortunately these SATA bridge cards have a very high failure rate as they are burdened with shuffle power and data.
Literally these little unreliable and fragile cards are the power conduits and the nervous system for all external HD data transfer.
SATA card as found inside a typical USB external hard drive
The assumption that the hard drive is bad when its not!
Countless 1000s of good external hard drives are thrown away each year because the owner thought the HD was bad when it fact it was the SATA bridge card which had failed. This card is removed in a matter of mere second once an external USB HD is cracked open from its plastic casing to reveal the bare HD and the attached SATA card which attaches between the HD and the USB cable.
To complicate this problem, even many computer professionals do not know that there is a very easy solution to the “failing or dead HD” issue since the hard drive itself is very likely just fine.  Its astonishing that so many highly educated computer repair persons are unaware of this high-failure part, but this is mostly due to the fact that they do not juggle 100s of hard drives and know that of the iceberg that is a “external hard drive failure”, the mostly unseen majority are not a HD failure at all, but a bridge card failure.
To add to this great misunderstanding is the fact that people assume that "likewise symptoms seen on an external HD are the same as seen on an internal HD, therefore also the external HD must be bad". This is a compositional fallacy of logic. Since internal HD do not have a SATA bridge interface, to conclude similar symptoms "indicate the same failure" is misplaced and incorrect.
This is all not to say that HD do not fail, they do indeed, and I have seen many 100s of dead and failing hard drives.  Hard drives even under ideal conditions have a life expectancy of around 4-8 years due to ferromagnetic depolarization from entropy.  But of the mountain of symptoms that are seen as “hard drive failures” in comments, posts, and hearsay, half or more of these are not a HD failure at all.
Once your rescued hard drive is removed from the bad SATA card
You have several options, but the purchase of a $20 HD enclosure is one option, another is having a HD dock, however this eliminates the former portability in a 2.5" small HD.
Remember that 3.5” HD require power, which means you need either a HD dock, or a powered SATA card kit as seen at top left in the picture below. 2.5” HD get power from the USB port itself.
Just remember that the serious downside to the low cost external HD enclosures is THEY TOO contain these SATA cards, and what is worse the cheap ones will fail, often, much quicker than the original factory one did! In which case it is recommended you buy a quality HD USB enclosure
Rescue tools to use with your extracted HD for data recovery

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