I know that this is a bit late. However, as a rule of thumb I would say no. While a quick search didn't reveal any connected side effects with birth defects or problems, there are a lot of issues to consider. The side effects in general can be very harsh including heart problems, liver problems, and more.
The best thing you can do when extreme pain happens and you are pregnant is to call your doctor. Only he or she will be able to prescribe a stronger than Tylenol pain medication that is safe for the baby. It is also possible that you will have to consider taking something that isn't safe with their watchful eye looking out for problems.
If you aren't wanting to involve your doctor (which I really do recommend since it could be a problem throughout your pregnancy) you can take Tylenol (or acetaminophen) as recommended on the bottle and lay down with a heating pad or a hot water bottle. You may want to alternate that with cold as well.
However, I can't emphasize enough that talking with your doctor is your best bet.