4 month old sleep problems

My four month old daughter is having problems sleeping during the day. She naps three to four times throughout the day but only for 30 minutes a time. She will sleep longer, 1-2 hours, if I wear her in an infant carrier. She sleeps okay at night. She has slept for 7 hours once, but then returned to waking every 3 hours the next night. At her birth I was given magnesium sulfate which did get to her though breast milk. She has been treated by an accupuncturist and has this cleared now. She was also treated for fear of being alone. My water broke and I did not deliver her for three days. Now she is teething. She is drooling constantly and has two swollen lumps where her canine teeth will be. She has been teething for almost two months. She often wakes up screaming. She is very pleasant when awake, but gets tired from lack of sufficient sleep quickly in the daytime. She is sleeping about 10 hours at night, but waking every 3 hours to eat. She is very restless when sleeping. She tries to suck her thumb but is unable to self-soothe yet. She has been taking Hyland's teething tablets for teething. This gives her some relief, but when I put her down to nap she wakes within 30 minutes or so.