Is my Stylus damaged?

I assume that was with the record sinning, and stylus repeating in the end groove? That could be bad - because of the grime that collects in the groove and rubs against stylus without cleaning cycles to break it up. Possibly much worse that equal runtime in normal playback, but at least it's a lower linear velocity, and 2 hours really isn't TOO bad. I remember reading a guy posting here about leaving the stylus running in end groove for a full 3-day weekend, and sadly he reported that the stylus was toast. 

I'd give it a listen and see how it sounds.If it sounds great but you're still concerned, you could send it to a retipper for evaluation. Personally I'd be pissed at myself if I did this, but I think it might be OK at 2 hours.

Please. Reality check: 2 hours is 2 hours. Cart good for a thousand easy. Not to mention runout is zero signal, much less wear than playing music. So chill.

Over the decades I've left my share of needles dancing around lead out grooves for a couple or three hours.  Two or three times I stupidly let a record spin around all night.  It definitely spun my brain around a bit, but it never physically harmed a thing.

You wore in a deeper runout groove, that’s about it. Next...

I seriously doubt any damage done. 

Fully Manual TT: I tried some inexpensive after-market lifters, no success, then bought this excellent auto-lifter

https://www.amazon.com/gp/product/B07HKX6WL7/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

love it, however, you need room between the edge of the platter and edge of the arm mounting plate. Some TT like my JVC, many Denon's have a wide rim around the platter, reducing available space for placement. Some have enormous arm plates.

It fit between my JVC TT81 Rim and my long arm's small base, but no room for it between my 9" arm's base and platter edge because the shorter arm hole is closer to the platter, reducing available space.

It should be OK.

jili12, 2 hours? That's nothing. I left it running all night once! The cartridge is fine and no I did not cut through to the other side. 

Well, thanks to all for your comments.  It sound OK so I guess it will be fine.  Have not been able to find tone are lift that will work with my Turntable, it is a Rega RP8.  Any suggestions?

I left a 17D2 running in the lead out groove for two weeks while I was on holiday in France. I came back to a ring of vinyl swarf, just the excuse I needed to exchange it for the D3. I do try and catch that record before the centre groove since then.

Hope that makes you feel better.

For that very reason, I’ve gotten a tonearm lifter with every table I’ve had so far - on table number three. The Little Fwend has worked best for me, although a little pricey ($249), it is built better than others IMO. Peace of mind - incase I forget or pass out listening to tunes. 

Clean the stylus or not.  The speed of the runout groove is slow so not that much distance would have been covered in two hours.  It would be like less than two hours of regular play except that there are no ripples in the groove to cause wear.  

...I really hate it when my lp's are sinning without me....that repetative *sic sic sic sic sic sic*, you Know they're up to no good....

...nasty stylus, rubbing that groove....makes one jealous, 'why can't I keep it up That long....?' *sigh*

I use one of these https://www.amazon.com/Audio-Technica-AT6006R-Safety-Raiser/dp/B07HKX6WL7/ref=asc_df_B07HKX6WL7/?tag...
It is $100 less than the Little Fwend and it works fine with medium to low compliance cartridges. The only caveat with these is not forgetting to cock the device. If you forget the record will skip at that point forever.  

Thxs for the suggestion on the tone arm lifter.  I have not been able to find one that works with a Rega 8.  Any suggestions would be appreciated.

see if your Rega is on the Little Fwend list
https://www.littlefwend.com/list-of-compatible-turntables-for-little-fwend

+ 1 for little fwend , have the disco fwend on my sl1200 ..

No.....if it looks centered and ok, just play a record