In most cases there is nothing to worry about. What you smell is the dust that was dislodged during the lamp installation process. The new lamp will be hotter that the old lamp and dust burns away when the new lamp is first turned on. You can eliminate some of this and improve the life and operation of the lamp by carefully vacuuming the inside of the TV or projector prior to installing the new lamp. Do not use canned air, as it only relocates the dust in undesirable areas and may impede the performance of the TV or projector.
When installing a projector lamp the lamp should fit snuggly but should not have to be forced. You should only require one hand to install a new lamp. A good connection is required if the projector or TV is going to work properly. You should be able to attach the lamp to the TV or projector with the installed screws. This insures that a good connection is made. Not doing so, may mean an improperly seated lamp, creating a possible fire hazard.
Most projectors are designed to turn off if it becomes too hot. The causes of overheating are usually clogged filters/vents or a defective fan.