Beginner please advice - Chest press but shoulders hurt?

Hi all, I am 31 and haven't weight trained for good 6-7 years due to personal problems. I've always have been broad built but do have a belly & a saggy chest. Since been cleared by my docs, I've just started (3 days in) doing cardio and weights at my local gym. I've been using the butterfly machine for my chest but the problem is that my chest muscles DO NOT hurt whatsoever but my shoulders kill and just give up. I do 3 reps of 15 and have a 20-30secs rest in between. I tried doing the bench press today and the same happened - shoulders killed like mad. I eventually give up due to arms having no strength and my muscles do not burn like I've read on many forums. I've been eating a lot of protein food like chicken breast, cod fillet - all steamed.

So my question is that; does the above sound right with my shoulders hurting and not my chest?. I would be very gratefully if someone could help me or advice me.

Thank you all.

I am going to suggest you have been using bad form ( its only a suggestion )

Probably lifting and contracting too quick also as you seem to be hitting every other muscle group to failure except the intended target.

Get a training buddy or even someone who works in the gym to help you as its pretty hard telling you where you are going wrong without actually seeing what you are doing.

You should be having more rest between sets 2 - 3 mins to allow your muscles to recover enough this is probably the main reason for the smaller muscles being smashed to bits before the larger muscle can really get fatigued

I am new too (about 6 months in), but would say that what your experiencing is correct.
When you train a muscle group it also effects another muscle group.
Butterfly machines will effect your shoulders as well as your chest, where pressing will effect your shoulders, triceps and chest.
The weakest link in this exercise will be the first to feel it and give up, so i guess your weakest link is your shoulders and then triceps. As these get stronger you will manage better and they will hurt less, allowing the next weakest link to take the pain, which will probably be your chest.
 
As i said, i am only new to this myself, but i experienced the same thing, and still do on an incline press to an extent.