I am experiencing the same with DDs sleep but she is a bit older than yours. Teething can start from 3 months. My DD has had a week of crying, restless sleep, waking an hour into night time sleep and all sorts of unusual habits. I am putting it down to teething as she is not ill but is not always settled even when picked up (ie screaming continues). As suggested take her temp to double check. I understand that fully breastfed babies don't get ear infections. My DD is also worse at night and when lying down.
Yours does sound like it, but could be wrong. With teething she may have symptoms now but you may not see a tooth for weeks. Check everything else (hunger, wind, nappies, tummy pain etc), if worried see a GP (they never mind checking babies) and if no answer, then perhaps it is teeth.