A few things youv mentioned gave me pause, and made me feel like I should add a few notes and bits of advice (take or leave them, but definately consider)
Your balls feeling cold when they are tied/bound - While you are sort of correct in that you can continue after/during this feeling, be aware that this is a sign that you should remove (at least just for a few minutes if your having a lot of fun...lol) the binding quite soon. Also, coldness AND and them feeling even slightly numb to normal touch (gently scratch with your nail, or fingertip, and if it feels different/odd/weird/etc), is a definite warning sign to remove the bindings imediately.
Continuing after the pain/sensation made you vomit - While there is nothing wrong with heavy CBT, and the feelings in your stomach indicate that this was HEAVY, continuing afterwards was definately a risky move. The amount of force/energy applied to your balls for this to happen, while not unheard of or directly "bad" (depending on your preferences and limits), should be the maximum you should endure safely during any single play session.
Being pushed by your play partner into going beyond your limits and/or pain/safety threshold - I think the other comments made above made the general consensus on this pretty clear. Trust and Safety are paramount. If you at any point say that you cannot, or are worried to, continue then the other person should not force or expect you to with out at least discussing, questioning, or otherwise making an attempt to discover the reason. Are you at your limit and can possibly be pushed just a little bit further (pushing of your limits is fine.....within reason and done VERY carefully). Is there a sensation/feeling, or new pain you are feeling, that makes you think damage is done or about to be done? Are you no longer having and fun/excitement form the experience in ANY form (doing something you may not like, but enjoying the feeling that you are pleasing or giving pleasure to the other person, is a common example) and would like to change gears?
Significant pain and phsical signs of damage/injury the following day - Go to a doctor as fast as possible.....I may heal, as you seem to indicate that it has, but 2 points to consider:
1 - Has it healed correctly, and is damage done that you can no longer feel or have gotten uesed to over the last few days?
2 - What if it the damage was continuing to increase (internal bleeding, damaged blood vessels causing lack or flow to parts, tearing/rupturing to vital parts that can be fixed if caught early, etc), or needing fast attention to prevent permanent damage?
Finally...the most important point when it comes to CBT play. KNOW YOUR LIMITS - I dont mean your "limit" limits. I meant your physical limits. Example:
You dont start weight based CBT, by tying a 10kg weight to your balls and dropping it from chest height
You start with smaller weights, hanging first, and then small drops, swinging, and squats (floor, hanging, floor, hanging...etc), and work your way up until you find out how much you can (un)comfortably take, without damaging or "hurting the not-fun way" your precious dangly bits (you only get 2, so you dont want to lose them...lol). The same goes for all forms of CBT 
I hope this helps both you, and anyone else who may find it usefull
On a personal note....I really wasnt to keen on this little fact you wrote :
But was happy to read a moment later, that you had been honest and forthright that some limits would remain unbroken. It is almost unheard of for someone to break all of their limits in my opinion, and so expecting it of someone so soon into a play partnership....she said that she would only meet me in real life when i have no limits left
Anyway, hope I helped