Babies may be prone to sore gums when they are teething, and can get restless or irritable, and even start stop sleeping or feeding badly which can result in problems digesting food and/or loose stools. Teething doesn't cause a baby to become really ill though, so any sick child should be seen by a doctor - and not pass health problems off as just 'teething'.
When a baby seems cranky, has sore gums and dribbles a lot, there are some things that you can do to help.
Try giving baby something to chew on. There's a good selection of teething rings on the market - but make sure they are made of soft material and are big enough so that there is no danger of choking. Some parents/carers find that teething rings containing fluid which can be cooled in the fridge are best. Milk, cooled boiled water, or very diluted sugar-free fruit juices may help - sweet drinks do not. If baby wakes at night and is irritable, you can use a mild pain reliever - preferably sugar-free. Ask your doctor or public health nurse to recommend one. Avoid ointments which numb the gum unless your dentist recommends them.
Not all children need soothers or pacifiers. If you feel the baby needs a pacifier it is important to make sure it is of the correct design. An Orthodontic type one is the most suitable and wean the baby off it as soon as you can as it can cause long term adverse effects on the way a baby's teeth grow. It's also advisable not to dip the soother into sugary liquid (honey, jams or syrupy medicines) to encourage the child to use it.
Babies get a lot of pleasure and satisfaction from sucking things - including their own thumbs. There is no real harm in letting them suck their thumbs. Most infants will stop of their own accord. You can expect children to have given up sucking by the age of 4 years, however it can go on longer, as thumb sucking makes a child feel conted and secure.
Thumbsucking is only really a problem if children go on sucking their thumbs after this age. Some children suck their thumbs very hard. This can pull their teeth out of shape so they should be helped to give up. To help a child to give up sucking, where possible encourage other activities instead.