My girlfriend is pregnant and has a severe toothache. Can I give her ibuprofin?

Yes you should. Your girlfriend should get pain killers to take care of her pain, it is safest during the second trimester as most fetal organ develop during the first trimester. She can get necessary x_rays anesthetic, filling or extraction even if she is pregnant, postpone all elective procedure till after the pregnancy, no need to suffer. Hope she get well soon.
Not recommended. Ibuprofen is a non-steroidal anti-inflammatory drug (nsaid). They are not recommended during pregnancy. An obstetrician should be consulted prior to taking medications during pregnancy. A topical tooth pain preparation should be considered until a visit to a dentist can be made.
Tylenol (acetaminophen) better. Tylenol (acetaminophen) is generally safe in pregnancy. You can also use topical clove oil to reduce pain. Real answer is to see a dentist & have the problem fixed.