This may not be what you want to hear but so so many babies begin with 2-2.5 hr intervals - it is normal. Your night times with 3-4 hr intervals and the occasional 5 hour are textbook. However not everyone is so lucky.
Many people start on an EASY which is less then 3 hours.
I wouldn't personally say that feeding 2-2.5 hours is an indication of a growth spurt and in my experience growth spurts do not last longer than a week. I also wouldn't see 'relentless crying' as a feature of a growth spurt - sorry if that doesn't sound very reassuring.
We started with 2-2.5 hour intervals, with 2.5-3 hours at night (occasional 4). By around 3 months we were more like 2.5-3 hours. We never made it to 4 - not everyone does.
To encourage longer intervals you can ensure you are feeding him effectively by burping him well, if he breaks off encourage him gently back on if he will take it, making sure your latch is good and you are hearing swallowing sounds and not restricting time at the breast (e.g breaking him off after a certain number of minutes).
I would not advocate trying to 'stretch' him to the next feed if he is exhibiting clear hunger signs and seems in need of feeding (I'm not saying you are doing this). He is developing your milk supply and it's important to learn the ways he is communicating with you. Too much 'stretching' to the next feed can leave you with supply problems in the long-term. Learn his cues as Tracy tells us to and you will be fine. His pattern will naturally emerge and then you use his natural pattern to begin your first EASY. Once EASY is up and running the intervals will naturally start to increase. When growth spurts do occur then you may need to use some flexibility - some people use a EAEASY activity - to make sure your milk supply keeps up with him.
With the crying, I would trust your instincts - if it doesn't feel right to you then maybe get a second opinion to rule out a possible problem - like reflux.
There's some stuff about growth spurts here:
https://babywhispererforums.com/index.php?topic=64627.0