DWP waiting time?

I have been claiming Income related and Contribution based ESA for over 15 years. At the beginning of December I received a n inheritance that put me over the savings limit for income based ESA. I wrote to the DWP to tell them on the day I received the money. I asked to remain on contribution based ESA but cancelled my income based. I heard nothing for the next month, so wrote again at the beginning of January. I have still heard nothing, and am still receiving the same amount of ESA. I don't know if this is a normal amount of time or if something has gone wrong. I cannot use the phone and I am now panicking that they will say I am fraudulently claiming. Thank you