We have sex every time using condoms . Just so happens that last night we used 3 . The first one he had came in and we threw it out . We continued and used two more and both broke :( is there anything we should worry about . He didn't finish. The only time he came was in the first condom and we threw that away .

You had unprotected sex. Yes, I would worry.

You had unprotected sex. Yes, I would worry.
As soon as they broke we changed them we didn't wait

As soon as they broke we changed them we didn't wait
What was happening between the time they broke (how did you know?) and new ones put on? Sperm must have been released inside you.

ANY time there is penile insertion, there is the risk of pregnancy. So if you do not want to be pregnant, then you shouldn't have sexual intercourse. If you are worried that you might have been impregnated, that is a valid worry given the circumstances.

What was happening between the time they broke (how did you know?) and new ones put on? Sperm must have been released inside you.
Both times they broke during intercourse . The first one broke and my boyfriend noticed I didn't , and we immediately changed condoms . The second one broke and I heard it pop and he pulled out and trashed the condom as well . He didn't yet

You really need to read up on pre ejaculate which was present and which can cause pregnancy.

Don't you understand that none of that can change our answer. You had intercourse. Therefore you risked getting pregnant. Because of the issues with the condoms, that risk increased. So the answer to your question is yes, you should be worried.

It doesn't matter that he thinks he didn't ejaculate. It doesn't matter that you changed the condoms quickly. All those things can reduce your risk, but not eliminate it. As soon as you let him enter you, your need to worry about getting pregnant existed.

"should I be worried ?"

Yes. Someone is selling you breakable condoms!

Oliver, have you ever considered law school?

What again? I've already completed it once. Well that is what they told me anyway.