My tires look like that on the low profile rims I use. If you added air to the tube (I do) you may have put too much in. Try letting some air out. Then just work with your thumbs until it goes in. You have to count a millimeter as a big victory. But it will go. Check often to make sure you are not pinching the tube and that the tube is not already caught between the rims bead seat and the tire bead some where else on that side.

If you added more rim tape or a rim strip, it may be taking up room that the bead of the tire in the rim wants so it can give room for the part of the bead you have not gotten into the rim yet. I think using tools is dicey, but I have resorted to levers when desperate. But that frequently also wound up causing a tube puncture.