Picture would be good.

Growing in compost? Poor idea. Compost has very little in the way of nutrients. Add some complete fertilizer.

The bagged compost may be the problem rather than using a typical seed starter medium, no telling what level of nutrients are available from that source unless there are numbers listed on the bag. The window sill should supply at least 6 hours of direct sunlight for good exposure and to prevent legginess and damping problems.

If the OP is in the U.K. which I'm wondering about, given the growing on a window sill and no mention of lights, 'compost' could just mean potting or seedling mix. Unless OP has a greenhouse it's too early to start tomatoes here. A pictures would certainly help. And a location.

To be specific, compost contains some nutrients, but most of it is in slow-release form. Seedlings want right-now nutrients. If there are NPK numbers listed on the bag, and they aren't from added fertilizer, they really don't mean much. And yes, windowsills are usually poorly lit, and might be cold as well.