Gaining

It sounds like ice cream may be a problem if you have sensitive teeth.

I would recommend puddings, yogurts, not the "lite" variety, but the regular. Peanut butter and Nutella are high calorie and quite tasty.

For less sweet, mashed potatoes are a good choice, especially with lots of butter, ranch dressing or heavy gravies.

Good luck.

anything full-fat dairy: yogurt, cottage cheese, ricotta, milk of course. Suuuppeerrr soft cheesees, even better if you can soften/melt them.

Avocados!

Mash up bananas, make smoothies with that and peanut butter and the milk. Get hawaiian rolls and dip them in soups - but you may have to puree chunky ones if your teeth are in bad shape.

Have you been examined by a dentist? "Sensitive teeth" is more of a genetic thing than environmental/diet unless you mean other problems. As someone with dental issues, it's worth getting your teeth examined at the very least, because whatever problems you have will only get worse.

Avacados are very soft and very fattening