Can I get esa, uc and pip at the same time?

You could consider a claim for PIP so long as any disability you have has been for 3 months, & expected to last for at least a further 9 months. As far as PIP goes, it's not about any diagnosis, but rather how your disability affects certain activities of daily living &/mobility. Have a look at the activities/descriptors that are looked at with PIP:  https://www.cambridgeshire.gov.uk/asset-library/personal-independence-payment-descriptors-and-scores-april-2022.pdf

About ESA & UC, see what poppy previously advised here: https://forum.scope.org.uk/discussion/104794/housing-benefit-on-esa