1. ISPs are within their legal rights to shape your traffic as per the terms and conditions you signed up. It's an industry practice. Whether they do it or not is a different story... Which brings me to point #2:
2. There's no proof that they shape/throttle IPTV traffic. ISPs in the UK block IPTV traffic due to legal laws about football matches and broadcasting rights. Anyway, the way the internet works is unpredictable - there's no proof PTCL is at fault here, but it could be another computer between you and the IPTV server acting up (that is just how the internet works - and not all computers or highways are perfect - some can be congested for whatever reason at different times. Imagining going from one end in Karachi to another - lots of variables come into play when you pick the default route because it's simply the best known route).
3. Will other fiber fix this? Depends. Maybe. Maybe not. If only one (or a selection of) website(s) doesn't (don't) work but the rest do at that moment in time on PTCL, then there's no guarantee it'll work on another provider if they use PTCL as their route. It's possible if an ISP using Transworld may not have this issue, but they could have route congestions with other websites. There really is no way of knowing unless you diagnose your route to the server yourself.
A small note: your connection to the IPTV host is one part of the connection process - the server/host then redirects you to another relay server where the channel is streamed from. There are several hosts that cater to multiple channels. Good luck checking all of them to see if it works (it's easy if it was one host, but I use IPTV and have gone through this facade, so I'm just trying to save you from the headaches - but be my guest if you'd like an educational experience).
Example:
You have your car and driver (PTCL), and you're in one end of Karachi (let's say West Wharf). You want to go to Bahria. You'd take I. I. Chundrigar, Shahra-e-Faisal and a bunch of other roads cause these are the main arteries known to you (or me, if my geography is correct, which it probably isn't). You step onto I. I. Chundrigar after entering your car and the driver (PTCL) takes you there. It's clear. You go to Shahra-e-Faisal, and it's clear - until you reach the airport and Malir. Oops - there's a traffic jam. It's moving, but very slowly, then it eventually gets fixed cause there was a water leakage on the road. Then traffic gets speedy and you reach your destination. That delay in between was the bottleneck in your entire route. That wasn't your driver's (PTCL's) fault because this was the only known major route to them, but KDA's fault for not being able to fix it at their end (or maybe the society looking after Malir was at fault).
You couldn't have seen this coming, right?
Had you opened up Google Maps (which you hadn't before taking your journey), you'd have known if another alternate route was available. Perhaps if some people earlier on at Shahra-e-Faisal set up a diversion, the driver would have bypassed Malir altogether and used another route, or skipped the water puddle on the road and landed at Malir and moved past that. Or if you knew, you would have said "don't go from Shahra-e-Faisal but go via Clifton (don't judge me - I don't know!). It'll take longer, latencies may be higher, but the speeds will be fine."
But your driver is slow to register requests because that's just how companies and technology can sometimes work.
Do you see what I'm trying to say? Routing on the internet works like your road or train networks. Changing your car from a Suzuki FX to a Prado won't speed up the water puddle experience at Malir when every other car flow there is choked and you stick to one knowledge map of a single driver.
This is how the internet works - except machines have limitations, internet pipes have capacities, and it varies with surges in demands. Either tell PTCL to take you via Clifton (instead of Malir), or get a new driver (a VPN) that knows other routes and go via DHA. Cause it turns out, convincing PTCL may be difficult (or slow), but getting a VPN (changing your driver) will be quicker and more effective.
Now does it make sense?