How do I cover up or get rid of these skin spots from my skin peeling after a sunburn?

Sunscreen. Daily application of a broad spectrum sunscreen will help prevent this predicament. Once a sunburn has occurred, it is important to use an oil free moisturizer to encourage recovery of the epidermal and dermal damage. Use of an oil free cosmetic may be used to camouflage any spots until the skin heals.

Related Questions

What's usually recommended for getting rid of peeling skin due to sunburn?

Use soothing lotion. Use any soothing lotion as the peeling will be followed by new skin and do noy try to peal the skin yourself.

How do I get rid of peeling skin from the sun quickly?

Moisturizer. Keep skin moisturized, but really there is not much you can do beyond that to help process.

Can I get rid of back acne and scars by skin peeling?

No. Acne on the back almost always requires a systemic antibiotic or stronger systemic therapy, in addition to some evidence-based topical treatment. Being a young adult is hard enough without having to accept an ineffective "pop / natural" treatment; today all acne can be treated effectively and this is your right.
It can be reduced. Before using any resurfacing modality the acne should be brought under control using medication. This is usually done with a combination of antibiotic, hormonal, and/or topical agents. Once the active acne is brought under control resurfacing techniques can reduce the scars but rarely clear them completely. The best results can be expected from laser. Chemical peels and dermabrasion can help also.