1997 Dodge Caravan At a loss

I was driving at 45 mph when the engine wound out and the transmission would not catch. I checked everything that I could on it but have limited knowledge on transmissions. I am able to drive in low and shift up and grab second but if I try to stay in 3 or drive it slips again.But as long as I hurry and shift back to Low than it will maintain the second gear. I am mainly trying to avoid transmission repair on a vehicle that is highly maintained and only gets used twice a week. Any ideas on troubleshooting this issue,ie. computer etc. ????