A lamp breaking is extremely unlikely to have any impact on your health. If a lamp breaks, ventilate the room for 30 minutes and remove the parts, preferably with gloves. Put them in a sealed plastic bag and take it to your local waste facilities for recycling. Do not use a vacuum cleaner.
Lamp contains mercury. Manage in Accord with Disposal Laws. See: www.lamprecycle.org or 1-800-555-0050