Coolant lose car over heating then cooling please help

Hi an thank u for reading this any help would be great so I fill my coolant to full level drive to work half way there my temperature gauge gos all the way too the top an says check coolant level then gos back to half way (normal ) an my heating doesn’t get hot till after this happens. While the car is runing I can see the coolant fill up an move around as if it’s bubbling. Can’t find any leaks not smoke coming out the back end no creamy stuff on oil filler cap just don’t no what it could be . Maby thermostat??? Maby water pump any ideas would be great please it’s going to cost a lot to change thermostat an water pump so would like to make sure it’s defo that before doing any thing. Thank u hope u having a nice day.