2003 Yukon Denali transmission problems

I have a 2003 Denali, the truck sounds great but when driving car revs high and doesn't sound like it wants to shift u till I let off the gas. Also doesn't feel like it wants to go higher than 3rd or 4th gear. I get up to about 40mph and it rpms raise high and it will not shift. No check engine light or codes are being thrown. Transmission fluid is full and doesn't smell burnt or anything. Any ideas other than to flush and see if that helps out, or if it a common problem that something has faulted...thank you for the help!

To eliminate guess work you should have truck scanned for transmission internal functions by a properly equipped transmission tech.

Rather not spend the money for that, I am mechanically inclined. But understand I could spend more money eliminating things rather than trying to have the problem found by a tech. Just wondering if anyone else has had this problem and it is a solenoid problem or something that can be solved by flushing the transmission. It is a 6.0 liter by the way.

Could be the transmission solenoids. Its worth a $50 try - change the oil in tranny and do the 1-2 2-3 solenoids while at it.