There could be a number of reasons for your missed period, one of which could be just a missed period - that happens sometimes. From what you have said, it would seem you would not have been fertile on 25th Dec, unless you ovulated late (not impossible).
- LMP 1st Dec; next due 4th Jan: 34-day cycle - Is that usual?
- If period were due 4th Jan it presupposes ovulation 21st Dec
- If you ovulated 21 Dec, you would not be fertile 25 Dec
- To be fertile 25th Dec, you would have to have ovulated 25th Dec or a few days later.
- If you ovulated 25th Dec, it would indicate a 38-day cycle. Has that happened before?
However, I am not sure what you meant about condom use. You said "had intercourse Dec 25 without a condom ... he pulls out using a condom".
Nevertheless if you are on birth control, then the likelihood of pregnancy is very low (if you take it correctly)
I hope this helps as a start